Using the criterion of the first and second derivatives, find the graph of the function c) F(x) = x - 8x² + 3 %3D

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: To Determine: Find the equation for the function f that has given derivative and whose graph is…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 −…

A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

Q: Find the derivative of the function. (Factor your answer completely.) f(x) = 4x2 In 3x %3D f'(x) =

A:

Q: A graph of y = f(r) is shown. In the same coordinate system, sketch a graph of the derivative…

A: To draw the graph of the derivative of the function

Q: 1. f(x) = x² at x = 3

A: Given: f(x)=x2 at x=3

Q: shows the graphs of the first and second derivatives of a function y = ƒ(x). Copy the picture and…

A: The graph of y=f"(x) is a linear function. So it is of degree 1.  The graph of y=f'(x) is a…

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

A:

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

A:

Q: Find the derivative of the function below using the definition of the derivative. f(x) = 2³ + 2

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A:

Q: Find the absolute extrema of the function f(x) = (x +9) 2/3 on the interval [-5,1]. Find the second…

A: To find absolute extremum of given function:

Q: Given f(x) : , find f'(-1) using the definition of a derivative. x-2 Provide your answer below: f'(…

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Q: Fill in each blank so that the resulting statement is true.

A: The slope of the tangent at a point on the curve is equal to the value of the derivative of the…

Q: 3. Use derivatives to find the critical points anc (a) f(x)= x³ – 9x2 + 24.x + 5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A:

Q: 3. Find the derivative of f(x) = 5x - 7 using the formula h f(x+h)-f(x) h

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Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Consider the provided function, fx=4x+13x-6 Find the second derivative of the function and then find…

Q: a) Find the derivative of g(x) = 3tanx - 4cotx. b) What is the value of g'() ?

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Q: Find f'(x) using the rules for finding derivatives. 3x-4 f(x) = x-4 f'(x) =

A: fx=3x-4x-4 We need to find the derivative of the given function.

Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

A:

Q: Using the definition, caleuhate the derivative of the following function. f (x) = 4-x²

A: Derivative: A function is said to be derivable or differentiable if lim∆x→0fx+∆x-fx∆x exists and…

Q: Q2/ Find the derivative of the function f(x) V4-x2 by definition

A: The derivative of a function f(x) with respect to x is given by limh→0fx+h-fxh. The given function…

Q: Given f(x)=√x + 3, find f'(-2) using the definition of a derivative. Provide your answer below: ƒ'(…

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: It is given that,f'x=-2x8-x2     and point 2,9 We have to find the function.

Q: Given f(x) = 2, find f' (1) using the definition of a derivative. x-2 Provide your answer below:…

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: To find an equation for the function f that has the given derivative and whose graph passes through…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) =…

A: Given: fx=x+2x-22=y To find the slope of tangent line at point (6,4) ,we need to find the value of…

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Find the derivative of f(x) = -4x 3+4 Provide your answer below: f'(x) = D

A:

Q: A graph of y f(x) is shown. In the same coordinate system, sketch a graph of the derivative function…

A: In the interval -4,-1, the function is decreasing giving a negative to positive slope.

Q: 12. Find f'(x) using the definition of the derivative.  f(x) = x3+ x

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Q: termine the derivative of the function g(x) In x+ 10 %3D r- 10

A:

Q: Select the correct graph of the derivative of the functionf (x) given below. -4 -2

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Q: Sketch the graph of the function ? = x3-6x2+12. Using the ff. First derivatives (critical…

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Q: Apply derivatives to determine the critical points of the function ?=?(x−6)².

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Q: f(x) = 2x² + 7x – 6. Find the first derivative of f(x) using the definition.

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Q: '(a): Using the definition of derivative, find the derivative of f(x) = x² + 1.

A: The given equation is: fx = x2 + 1 The derivative of this equation is found as follows:

Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: [4] For the Basic Absolute Value function f(x) = x, (a) state its slope (derivative) function (b)…

A: The absolute value function, |x| is defined as follows. |x|=xx≥0-xx<0   The graph of |x| can be…

Q: Using the First Derivative Test, what are the local extrema for the function h(x) = 3x3 – 9x2 – 72x…

A: It is given that,              h(x)=3x3-9x2-72x+9we have to find the local extrema of the function.

Q: Q2/ Find the derivative of the function f(x) =V5- x2 by definition

A: →When limit is of the form 00or∞∞ (Indeterminate form ) then L Hospital's rule is used . In this…

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: NOTE: Refresh your page if you can't see any equations. . the given graph is a parabolic graph and…

Q: Find the derivative of the function f(x) 3x2 – 12x by the definition of derivatives f(x + h) – f(x)…

A:

Q: What is the derivative of f(x) = -3? Do not include "f'(æ) =" in your answer. For example, if you…

A: Given            f(x)=-3

Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

A:

Q: Using the definition of a derivative, find f' (z) given f(x) = -r +4x +4x +2. (Do not include"f' (x)…

A: Given, fx = -x3+4x2+4x+2  We have to find the value of f'x

Q: 6. Find all relative extrema of the function h(x) = -3x5 + 5x3 using the Second Derivative Test.…

A: Relative maxima and minima