4. Determine all possible functions f(x) that satisfy the given conditions. (a) f'(x) = V¤ – 3 x2 (b) f'(x) = sec² x + 6e2¤ and f(0) = 5 (c) f"(x) = = 2 sin x + 12x, f(0) = 3 and f'(0) = –1

Q: 8. Find f'(x) for the function f (x) = (5x² + 3)4

A: ddxfxn=nfxn-1f'x

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A:

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: 3. Find f. (a) f"(x) = x + 12x² %3D

A:

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find f. f(x) = f ''(x) = cos(x), f(0) = 4, f'(0) = 5, f "(0) = 7

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Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: Find the function such that f'(x)  = f(x) (1- f(x)) and  f(0)  = 1/2

A:

Q: If f(x) (1)? = 2 x² + 3x x+1 " then what is

A: Given: f(x)=x2+3xx+1

Q: Let f(x) = 5 sec(5x) f'(x)

A:

Q: Find f if f"(x) = 0, f(0) = 2, f'(0) = 1

A:

Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: If f(x)- Vu² - 1 du, then what is f'(3)?

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

Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

A: We need to find f(3.8)

Q: Given f''(x) = 3x – 6 and f'(– 3) = – 2 and f( – 3) = - 1. Find f'(x) = and find f(4) =

A: