Consider f(x) = x²(7 - x)5. (a) Find f'(x) and factor your answer completely. f'(x) = 67228x³ - 60025x4+20580x5 - 3430x6 +280x7 - 9x8 (b) Find all critical points of f(x), then use an appropriate derivative test to determine local maxima and minima. f(x) has ---Select--- (smallest value) f(x) has ---Select--- V at x = at x =

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A: Given equation is x3=-4yfx+siny+1 Product rule of differentiation states that: ddxuv=vddxu+uddxv…

Q: Find f. r'(x) = 1 + 3Vx, (9) = 69 f(x) V 2x + 4x + 4635

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Q: ƒ' (4) = If f(x) = 3√√√x(x³ − 2√x + 2), find f'(4).

A: Given that

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A: Using product rule and chain rule of derivative,

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A: f(x)=-(x-1)2 = - (x2 - 2x + 1) = 2x - x2 - 1

Q: Find f'(x)) D f(x) (2) f(x) 3x³ +5x²12-2 2 6x -3x + 2x12 2

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Q: Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values…

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Q: Consider the function. Find f'(x). f'(x) = Find F"(x). F"(x) = Find f"(-7) and f"(3). F"(-7) f"(3) =…

A: Given query is to find indicated derivative and the point where it's concave up and down.

Q: Find f such that f'(x) = 2x² + 7x-4 and f(0) = 7. f(x) = ...

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Q: Find f such that f'(x)=6x-5, f(6)=0. f(x) =

A: Just i have integrate the given function and then use the given initial condition and then find the…

Q: f(x) = 9x+sqrt(x+82) Find (f-1)'(0) = ?

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Q: find f'(x) given that f(x) = (2x5+2x2-3) (3x3-2x2 + 4)

A: The function f(x)=2x5+2x2-33x3-2x2+4, we have to find f'(x).

Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

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Q: comput and interpret f'(1) for each function below (a) f(x) = 6x2 + 3x − 4            (b)f(x)=10…

A: a)f(x)=6x2+3x-4differntiating both sidef'(x)=12x+3put x=1f'(1)=(12x1)+3=15f'(1)=15  answer

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Q: Find f such that f'(x) = 2x² + 9x - 8 and f(0) = 9.

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Q: Test f(x) = (x3/3) +2x2-5x+1 for relative extrema, using the second-derivative test where possible.

A: For a given function,f(x), at relative extrema x=a, f'(a)=0.The second derivative test is applied to…

Q: Let f'(x) = ƒ(x) = (8x² − 8)^(2x² — 6) ¹²

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