For the function f(x)=x^2 e^−2x, find:    (a) the local and absolute extrema.    (b) the intervals of increase and decrease.

Q: Find the indicated derivative. x2 Find f(3)(x) if f'(x) = x2 + 6 f(3)(x) =

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Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: C.) approximate derivative; 5.) y = 2x 6.) y = x +34x + 4000

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the derivative. f(x) = tanh(x) f'(x) =

A: Using chain rule of differentiation

Q: Apply the second derivative test to find all relative extrema. - 5)² (a) f(x)=(x

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Q: pret 30. f(x)= e2! dt 2-x

A: Given that: f(x)=∫2-xxexe2tdx

Q: If y = I, find f' (8) and f" (8).

A: This question is based on differentiation of function.

Q: Find the derivative y=arctan(square root 1+x/1-x)

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Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

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Q: Use the first derivative test to find and classify the relative extrema of x2 +8x+ 16 f(1) = For…

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Q: Find the derivative of the function. y = x2x + 7     Thank you very much for your help.

A: Find the derivative of the function

Q: Vith its derivative. A. f(x) S'(x) D. B.

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Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: what is the differentiate of f(x)=ln x

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Q: Find all possible functions f with the given derivative.  f'(x)= ex

A: The given derivative function is,

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: Differentiate the function   f(x) =    1/  ln x

A: Given function is fx=1lnx We know that 1an=a-n So, given function can be written as fx=lnx-1 Before…

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Find the derivative. y = ecosh(8x) y'(x) =

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Q: sinh(3x) g(x) 3

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Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Find the derivative f(x)= Inlex+9)

A: To find: the derivative of f(x)

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: Explain why a positive derivative on an interval impliesthat the function is increasing on the…

A: On an open interval Suppose  is a function on an open interval  that may be infinite in one or both…

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: find the second derivative and simplify the final result. 3. 4ln(Arctan x) = 1-y

A: The given function is 4lntan-1x=1-y It can be written as  y=1-4lntan-1x Differentiating with respect…

Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the formula for -…

A: Consider the function  g(x)=tan−1x3

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: Find the intervals of increasing and decreasing, and intervals of concavity for f(x)=x^2/3(x-4) Do…

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Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Differentiate the function. y=ln(x5sin2x)

A: Given function:

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: f(x)=2x^{2x}  f'(x): ? Please find first derivative

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Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

Q: Find the rate of the change of the function f(x)=-cscx-sinx

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Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

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Q: Find the relative extrema of f(x) = 4+ 40x – 5x? using both first and second derivative tests. f (x)…

A: Explained below

Q: Differentiate f(x)= (3x+2)^(arctan(x))

A: We can solve this problem using logarithmic derivative.

Q: find the derivative that function  f(x)=xsinx

A: Given,          fx=xsinx

Q: Find the derivative. f(x) = eX cosh(x) f'(x) =

A: First use relationship between hyperbolic function and exponential function convert coshx in…

Q: How do you find the derivative of function y=x^2-2radicalx/x

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Q: Find the derivative. f(x) = 4cosx + √x

A: Given function is fx=4cosx+x. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating…

Q: A bicyclist is riding on a path modeled by the function  f(x) = 0.04(10x − x2),  where x and f(x)…

A: given: A bicyclist is riding on a path modeled by the function fx=0.0410x-x2 where x and f(x) are…

Q: What do you look for when you need to match the graph of a function with the graph of its…

A: Observe the behavior of graph as the value of x increases.

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

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