Given the function f(x) = 3cos(x/2), find the relative extrema on the interval (pi, 7pi) using the First Derivative Test and the Second Derivative Test. Compare the results. Graph the function with the relative extrema.

Q: Find the indicated derivative. x2 Find f(3)(x) if f'(x) = x² + 4 f(3)(x) :

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Q: 1-x e) f(x) = 1+x

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Q: 2x f (x) = Vx+1

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Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: Find the higher-order derivative. f ''(x) = 18x3 − 34x2   f '''(x) =

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Q: Differentiate and find the second derivative. g(x)= ex(x3+2x) What is g''(x)=

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Q: Find the second derivative of the function.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Q1. Find the derivative of f(x) = 2x -- by using the definition of derivative.

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Q: For the function y = (9x2 - 27)/x3 , determine the increasing and decreasing intervals, and identify…

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Q: Using the criterion of the first derivative, find the graph of the function: F(x) = 114 (x*) + 4,…

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Q: Find the derivative of the function. f(x) = 8x

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Q: Find the derivative of the function f(x) = 3– + x² + 14. f'(x) =

A: Consider the function  f(x)=31x3+x2+14

Q: solve the derivative f(x) = e^3x / 1-x^3

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Q: Find the derivative of the function f(x) = 53x

A: Here given function fx=53x

Q: For the function f(x) x + x3, find all of the relative and absolute extrema using the first or…

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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: Find the indicated derivative for y=f(x)=9-x^2

A: Answer and explanation is given below...

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

A: Given, f(x)=9x3+1x On differentiating both sides w.r.t x we get:…

Q: Find the derivative of the function using the definition of derivative. 1 f(x) x² - 36

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Q: Find the derivative of the function. f(t) = arccsc(−9t2)

A: To find: the derivative of the function ft=arccsc-9t2. Solution: since, the derivative of arccscx…

Q: Use the first derivative test and the second derivative test to determine where each function is…

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Q: What is the fourth derivative? x^12+1

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Q: find value of derivative f'(a) for the given value: f(x)=x2 + 3x + 1, a=3

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Q: Use the Quotient Rule to find the derivative of the function. x2 h(x) = %3D X + 2 h'(x) =

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Q: Given the derivative f'(x), find the x-value for all relative extreme for the graph of the original…

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Q: y = csch /sec(x³ + 2)

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Q: y = x* – x

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Q: Given f(x)= (x+ 2) Find f'(x) by using the definition of derivative.

A: fx=2x+22

Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

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

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Q: Find the derivative of the function and evaluate the derivative at the given x-value. f(x) = 5x +x…

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Q: find the derivative of the function f(x)=6x

A: We have to find the derivative of given function.

Q: 23: USE THE DEFINITION OF THE DERIVATIVE to find the derivative: :9(x)=3

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Q: derivative

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

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Q: Find the indicated derivative. 8. f (x) = x* – 2x³ + x² – 4 x – 20 find f*(x). -

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the…

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Q: the derivative () of = f(x) = 2

A: Please refer to the image below

Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: f(x) = V4x +5 , use the definition of the derivative to find f '(x).

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Q: Calculate the derivative of the function, then find the value of the derivative at the specified…

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Q: Find the derivative of the function. f(x) = X + 8

A: Here, we need to find the derivative of f(x)=xx3+8. So,          f'(x)=xx3+8' Apply the Quotient…

Q: Find the derivative of the functionf(x) = (2 – x*)

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Q: For the implicitly-defined function, calculate the derivative with respect to x. + y74 = -6y ,3/4

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Q: Find the derivative of the irrational function y=2√x−33√x.

A: Given: y=2x-33x

Q: Find the derivative of the function f (x) = Vx /x – 6.

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Q: 33. Solve for the second-order derivative of the function below. Y = x 3x3 За

A: Differentiate two times wrt x

Q: find the derivative f(x) = sin (x^−3/e^-x )

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Q: Find the local extremes of f (x) = x³ +2x+ using the first derivative test.

A: Given,         The local extremes of fx=x3+34x4 using the first derivative test.

Q: Find the indicated derivative. f (x) = (x³ – 5x + 2)(x² + x – 7); find f"(x). %3D

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