The function h(x) = (x + 8) can be expressed in the form f(g(x)), where f(x) = x, and g(x) is defined below: 9(z) =

Q: The derivative of f(x) = 3 (22 + 4x) is - O 3x + 12 O -3x-2(2x + 4) 3x-2(2x + 4) O 3 -3x-3 (2x + 4)

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Q: Consider the function f(x)=2x3+9x2−108x+5,  −6≤x≤4f(x)=2x3+9x2-108x+5,  -6≤x≤4. Use the derivatives…

A: Given, f(x)= 2x³+9x²-108x+5 -6<=x<=4

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: Find the local maximum and local minimum values of f using both the first and Second derivative…

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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 absolute maximum and minimum values of the function f(x)-cos²x-3sinx on the interval 0≤x≤7.

A: First I have find the derivative of the given function and set them to zero .Solved them to get the…

Q: The derivative of f(x) 4 (x2 + 3x) is O -4x3 (2x + 3) -4x 2(2x + 3) 4 O 4a-2(2x + 3) 4.x + 12

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Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: The function f has a continuous second derivative, and it satisfies f(-8) = 5,f'(-8) = 0 and f"(-8)…

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Q: Find the derivative of the algebraic functie c3 – x³ c3 + x3 c is a constant. f(x) %3D 6r3 3 (3 +x³)…

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Q: For k(x)=(x−1)(−x2−2x)(2x−2), find the derivative of k(x) using the product rule. Do not include…

A: Obtain the derivative of the function k(x) as follows.

Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)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: Use the Second Derivative Test to find the Maximum and Minimum value(s) of the function 3 f(x) x* -…

A: We have the given function as fx=32x2-4x+lnx For maxima/minima, we need to calculate f'x as…

Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

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Q: Let f(x) = 4x^2 – 7x. Use the ɛ/8-definition of the derivative to prove that f'(2) = 9.

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Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

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Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: Let f(x) = 2x ^ 3 – 7x + 3x ^ 7 – 2. Find the 4th order derivative evaluated at x=2. A

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Q: Use the chain rule to find the derivative of f(x)=3e^−4x^9+3x^3   f'(x)=

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Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

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 product rule to find the derivative. f(x) = (3x - 2)(6x + 1) %3D O f(x) = 36x - 4.5 !3! O…

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Q: Let f(x) be a polynomial and g(x) = f '(x) be its derivative. If the degree of (f(x) + f(-x)) is 10,…

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Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (г) — 5x — 4 2. f (x) =…

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Q: Find the local minimum and local maximum values of the function g(x) = 6x2− 4x3 using both the First…

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Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: find f'(x) for f(x) = 2xtan-1 x - ln(1+x2)

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Q: (B) Use the first derivative test to find the maxima and minima for f(x) = 3. 5z2 + 6x +9. 2.

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Q: find all possible functions with the givenderivative. y' = -1/x2

A: Given: y'=1x2

Q: Find the derivative of the function f ( x ) = x2−10x+3 using First Principles.

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Q: f(x)=5e^−2x^3+8x^8 f'(x)=

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Q: Find the derivative: g(x) = 6x² e- X O g'(x) = 6xe (2-x) Og'(x) = -12xe** O g'(x) = 6xe (2-x) O…

A: We have to find derivative of given function.

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: Find the derivative of the following using the limiting process. f(x)= -4x2 + 5x

A: Given: fx=-4x2+5x

Q: f(x) = (x2 + x) (x* - 6x)3 %3D

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Q: Find the derivative of the function f(x) = 8x² – 14x by the definition of derivatives f(x+h)-f(x)…

A: Given function: fx=8x2-14x

Q: Find the first derivatives: 3. g(x) = (1 + 2x²)(x – x²)

A: As per bartleby guidelines we only give first question answers.

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

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Q: (2x-6) ¹² 3. h(x)= (3 + نمو)

A: The objective of the question is evaluate the derivative of the given function.

Q: For k(x)=(−3x2+2x−3)(x−2)(−x+3), find the derivative of k(x) using the product rule.

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Q: Find the local and absolute extremum for the functions over their domain: 2. f(x) = x3 + 4x2 – 11x –…

A: Given function is  f(x)=x3+4x2-11x-2

Q: Rewrite the function g(x) = ((x^2)-1)/((x^2)+2) so that you can solve for the derivative using the…

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Q: The function f(x) = 2x³ – 27x² + 108x + 9 has derivative f'(x) = 6x² – 54x + 108. f(x) has one local…

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Q: Find the derivative of the function using Chain Rule. f(x) = (2x-5) ¹ (4x+3) Given -2(12x-17) Answer…

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

A: here option C is true 6x-12