Calculus Graphing with the Second Derivative Examples of Curve Sketching 1 Answer Nallasivam V Refer Explanation section Explanation Given #y=x^32x^2x# #dy/dx=3x^24xAt x = 1, y = x 3 2x 2 = (1) 3 2(1) 2 = 1 2 = 3 Thus the graph of y = x 3 2x 2 is below the xaxis at x = 1 The important point here is that the graph is thus below the xaxis for all x satisfying x < 0 since to go above the xaxis the graph would need to cross the xaxis and it doesn't touch the xaxis until x = 0Exponential probability distribution Useful for modeling the lifetime of electronic components A continuous rv Xfollows the exponential probability distri
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Students were given the graph of a region R bounded below by the graph of the function f and above by the graph of the function g, where fx x x 264 2 and 4cos 1 4 g xx In part (a) students were asked to find the area of R, requiring an appropriate integral setup and evaluation Students needed to correctly evaluateHas a line by 2 and 3 B y > 2/3x 3 and y < 1/3x 2Graph of the parabolas, y = x 2 (blue) and y = (1/4)x 2 (red) The general charactersitics of the value "a", the coefficient When "a" is positive, the graph of y = ax 2 bx c opens upward and the vertex is the lowest point on the curve As the value of
Graph x/2 3Graph halfx 3Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreAbout Beyond simple math and grouping (like "(x2)(x4)"), there are some functions you can use as well Look below to see them all They are mostly standard functions written as you might expect
{y>−2x−2y≤x4 A system of 2 linear inequalities graphed on a coordinate plane The horizontal xaxis ranges from negative 5 to 5 in increments of 1 The vertical yaxis ranges from negative 5 to 5 in increments of 1Learn the steps on how to graph the equation of a line y = 1/2x on a Cartesian graph 58 jyoung So if you look at the equation you can see the yintercept slope yintercept ↓ ↓ y = x 2 The yintercept is where the line crosses the yaxis So which ever graph has 2 as the yintercept in correctIts more complex when the graphs have the same intercept but in this case this should be easy to find So looking at
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Graph exponential functions using transformations Transformations of exponential graphs behave similarly to those of other functions Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function f ( x) = b x \displaystyle f\left (x\right)= {bGRAPH THE EQUATION y = 1/2x 3/2 2) y = x 2 x 2y = 16 x= _____ y=_____ 3) 2x = 5y 3 6x 15y = 3 4) 5X 2Y = 36 3X 4Y = 6 Since I didn't understand what you wrote, I answered some of the problems as best as I can in what you meant Step 1 Just a quick noteGraph of y = 2x 1 If you knew at the beginning, from the "form" of the equation that the graph was a straight line then you could have plotted the graph more quickly In this case you only need to calculate and plot two points and the line joining these two points is the graph I
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The graph of `y=3x`, with the area under the "curve" between `x=0` to `x=1` shaded When the shaded area is rotated 360° about the `x`axis, Find the volume if the area bounded by the curve `y = x^3 1`, the `x`axis and the limits of `x = 0` and `x = 3` is rotated around the `x`axis Answer This is the region as described,Look at the graph The closer to 0, the greater the rate of change The further away from 0, the smaller the rate of change At every point of that graph, the tangent has a negative slope the derivative is always negative As we move from left to right,Start studying Solving Systems of Linear Inequalities Quiz Learn vocabulary, terms, and more with flashcards, games, and other study tools
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Learn how to use the Algebra Calculator to check your answers to algebra problems Example Problem Solve 2x3=15 Check Answer x=6 How to Check Your Answer with Algebra Calculator First go to the Algebra Calculator main page Type the followingGraph Inside the square root, you're subtracting 1, so the graph will move to the right 1 from the basic graph You're also adding −2 outside the square root, so the graph will move down two from the basic graph Before making a table of values, look at the function equation to get a general idea what the graph should look likeYou can put this solution on YOUR website!
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P1 FXS/ABE P2 FXS c07xml CUAU021EVANS 1936 210 Essential Mathematical Methods1&2CAS Quartic graphs The graph of f (x) =(x −1)4 3isobtained from the graph ofy =x4 byatranslation of 1 unit in the positive direction of the xaxis and 3 units in the positive direction of the yaxis As with other graphs it has been seen that changing a simplyGraph of the function y = 4 x is shown in Figure 3 x y xy = 4 2 2 normal tangent Figure 3 A graph of the curve xy = 4 showing the tangent and normal at x = 2 From the graph we can see that the normal to the curve when x = 2 does indeed meet the curve again (in the third quadrant) We shall determine the point of intersection Note that whenSelect a few x x values, and plug them into the equation to find the corresponding y y values The x x values should be selected around the vertex Tap for more steps Replace the variable x x with 0 0 in the expression f ( 0) = ( 0) 2 − 2 ⋅ 0 − 3 f ( 0) = ( 0) 2 2 ⋅ 0 3 Simplify the result
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Quadratic graphs Intermediate and Higher tier A quadratic graph is any graph which has an \(\text{x}^2\) in its equation We draw them in a very similar way to straightline graphs and willCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyA vertical translation A rigid transformation that shifts a graph up or down is a rigid transformation that shifts a graph up or down relative to the original graph This occurs when a constant is added to any function If we add a positive constant to each ycoordinate, the graph will shift up If we add a negative constant, the graph will
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Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Y=2x3 (red line) y=2x1 (green line) (graph 300x0 pixels, x from 6 to 5, y from 10 to 10, of TWO functions y = 2x 3 and y = 2x 1)We're told to find the x and yintercepts for the graph of this equation 2y plus 1/3 X is equal to 12 and just as a bit of a refresher the xintercept the xintercept is the point on the graph that intersects the x axis so we're not above or below the x axis so our Y value must be equal to 0 and by the exact same argument the y intercept the y intercept occurs when we're not to the right or
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Which graph represents the solution set of the system of inequalities?And the area of R is given by A R E A = ∫ c d w ( y) d y = ∫ c d ( r ( y) − l ( y)) d y EXAMPLE 2 Compute the area of the region in the plane enclosed by the graphs of y = 2 x and y = x 2 Using vertical crosssections we have that 0 ≤ x ≤ 2 a n d x 2 ≤ y ≤ 2 x so that the area of the region is How do you sketch the graph #y=x^32x^2x# using the first and second derivatives?
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All values that satisfy y < x 3 are solutions Which system of linear inequalities is represented by the graph?The zeros of a function correspond to the intercepts of its graph If has a zero of odd multiplicity, its graph will cross the axis at that value If has a zero of even multiplicity, its graph will touch the axis at that point If this is new to you, we recommend that youA graph of the straight line y = 3x 2 We can calculate the gradient of this line as follows We take two points and calculate the change in y divided by the change in x When x changes from −1 to 0, y changes from −1 to 2, and so No matter which pair of points we choose the value of the gradient is
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A graph makes it easier to follow the problem and check whether the answer makes sense Sketch the function on a piece of graph paper, using a graphing calculator as a reference if necessary Sketch the tangent line going through the given point (Remember, the tangent line runs through that point and has the same slope as the graph at that point)We see that all those solutions lie on a straight line In fact, every pair (x, y) that solves that equation will be the coördinates of a point on that lineOn that line, every coördinate pair is (x, 2x 1)y = 2x 1 That line, therefore, is called the graph of the equation y = 2x 1 And y = 2x 1 is called the equation of that line The graph of an equation, in other words, is theSolutions to Graphing Using the First and Second Derivatives SOLUTION 1 The domain of f is all x values Now determine a sign chart for the first derivative, f ' f ' ( x) = 3 x2 6 x = 3 x ( x 2) = 0 for x =0 and x =2 See the adjoining sign chart for the first derivative, f ' Now determine a sign chart for the second derivative
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Quadratic Graphs Complete the table of values for y = x2 2x On the grid, draw the graph of y = x2 2x for values of x from 2 to 4 2 2 Solve x2 2x 2 = 1 (6) Sorted it Complete the table of values (a) for y = x2 1 (b) for y = 2x2 2 NAILED IT Draw the graphs Finding the Area of a Region between Two Curves 1 If R is the region bounded above by the graph of the function and below by the graph of the function over the interval find the area of region Solution The region is depicted in the following figure Figure 3 A region between two curves is shown where one curve is always greater than the otherRelated » Graph » Number Line » Examples » Our online expert tutors can answer this problem Get stepbystep solutions from expert tutors as fast as 1530 minutes
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Function Grapher and Calculator Description All Functions Description Function Grapher is a full featured Graphing Utility that supports graphing up to 5 functions together You can also save your work as a URL (website link) Usage To plot a function just type it into the function box Use "x" as the variable like this• check by sketching the curve on your graphic calculator 11 y = x3 3x2 – 9x 6 12 y = 2x3 – 3x2 – 12x 4 13 y = x3 – 3x – 5 14 y = 60x 3x2 – 4x3 15 y = x4 – 2x2 3 16 y = 3 4x – x4 A Resource for Freestanding Mathematics Qualifications Stationary PointsSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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Algebra Calculator is a calculator that gives stepbystep help on algebra problems See More Examples » x3=5 1/3 1/4 y=x^21 Disclaimer This calculator is not perfect Please use at your own risk, and please alert us if something isn't working Thank youGraph y=x^33x^22x Find the point at Tap for more steps Replace the variable with in the expression Simplify the result Tap for more steps Simplify each term Tap for more steps Raise to the power of Raise to the power of Multiply by Multiply by Simplify by subtracting numbersAn online derivative calculator that differentiates a given function with respect to a given variable by using analytical differentiation A useful mathematical differentiation calculator to simplify the functions Just copy and paste the below code to your webpage where you
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