Determine where the graph of the function is concave upward and concave downward and find all inflection points of the function for  f(x) = (x-2)3(x-1)

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A: Now differentiating with respect to x, we get

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

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Q: Find the derivative of the function f(x) = -8x² – 18x + 23 by definition of derivatives f(x + h) –…

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Q: Find the points of inflection given the function: Given the function f(x) = 2x³+ 3x²-12x-9 Where…

A: For the inflection point, second derivative is equal to zero.

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Use the first derivative test to determine the local extrema, if any, for the function f(x) = 3(x -…

A: Given that a function f(x) and we find local extrema. For local extrema we do first derivative of…

Q: Determine the intervals of concavity and inflection point(s) for the function f (x) = 3x – 5x“ – 1 -

A: The given function is f(x)=3x5-5x4-1

Q: Find the slope and an equation of the tangent line to the graph of the function at the specified…

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Q: Show that f (x) = 2x2 -3 is an even function. Explain why itsgraph is symmetric about the y-axis.

A: Here given fx=2x2-3   A function is said to be an even function if f-x=fx Now…

Q: Determine the local extrema of the function f(x)=x2lnx.

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Q: Find the relative extrema of the functions f(x)=-4x2-32x-62. Identify any maximum or minimum by…

A: Given function is Differentiating f (x) with respect to x, we get Now, we will find critical…

Q: Find f'(x). 6. f(x) = 4x + 7x f'(x) = Compare the graphs of f and f' and use them to explain why…

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Q: Using the criterion of the first and second derivatives, find the graph of the function a) F(x) = x³…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 – 6x² –…

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Q: Using the second derivative criterion, find the graphs of the functions a) F(x) = x*– 8x² +3

A: Given- (a)  Fx=x4-8x2+3 To Find- The graph of the above functions using second derivative.

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

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Q: For the function f (x) = 2x° – 3x2 – 12x, use the First Derivative Test to find the location of any…

A: The given function is- fx=2x3-3x2-12x To find the critical points of a function- dfdx=0…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Use the Second Derivative Test to find all relative extrema of the function f(x) = 2x - 6x +7.

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Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: he derivative to determine whether the function is strictly monotonic on its entire domain and…

Q: Determine all of the relative extreme values of the function f (x) = 1 – (x – 2)- %3D

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Q: 3) Find the interval where the graph of f(x)= -2x' +3x +36x-1 is concave upward or concave downward.…

A: The given function is fx=-2x3+3x2+36x-1. Using second derivative test, the concavity as well as the…

Q: Using derivative, find the absolute maximum and minimum of f(x) = 2x3 +3x2 −12x on [−3,3]

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Q: Find the x-coordinates of all local maxima using the second derivative test. g(x) = 2° – 3x7 +2

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A: A Function f has a local maximum at a point x0 if the values f(x) of f for x 'near'x0 are all less…

Q: Find Domain and range of f(x)=x^x and graph it.

A: The objective is to find Domain and range of f(x)=x^x and graph it.

Q: Use the first derivative test to determine the location of each local extremum and the value of the…

A: The given function is f(x)=4xe-x The objective is to determine the location of local extremum and…

Q: Let f be a function with a second derivative given by f" = x²(x– 3)(x– 6). Find the x-coordinates of…

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Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: Find the x-coordinates of all points where the graph of f(x) = 2x^3+9x^2-168x+21 has a horizontal…

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Q: Determine the intervals of concavity for the graph of the function f(x)= xe^x. ( Enter your answer…

A: The graph is shown below::

Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

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Q: For the function, find all critical numbers and then use the second-derivative test to determine…

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Q: Find the equation of the slant asymptote for the function f(x)=x^2-x/x-2 y=

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Q: Find the relative extrema of the function and classify each as a maximum or minimum using the First…

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Q: Find the range of the function for the domain {−2,0,4}. Show your work. f(x)=5x2+4

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

A: Please refer the attached image for complete solution.

Q: f '(x) by using the definition of the derivative. f(x) = 4 – 6x2

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Q: Make a sign diagram for the first and the secon derivatives and then graph the function…

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Q: Find the interval on whih f(x) =x2-3x+8 increasing or decreasing

A: Given,        fx=x2-3x+8

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the…

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because…

Q: use the second derivative test to find and characterize all the relative extremes of f(x)=2x4-24x3+4

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 - 9x² –…

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Q: Find the derivative. f (x) 7.) f(x)==x³+2x²–11 x–1 +2x²-11 x-1 6.

A: We have given

Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Graph the tangent line to the function f(x) = –3x³ – 2x² – x + 3 at the point (-1, 5). Place point A…

A: Given that the function  is    f(x) = -3x3 - 2x2 - x + 3  Here we have to find the tangent line at…

Q: Find the local maximum and local minimum values of f using both the First and Second Derivative…

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