Find the unique function f (x) satisfying the following conditions: f" (x) = e3x f' (0) 1 f (0) = 1 (Enter exp(x) for e".) f (x) =

Q: 1. Find the general form of f if f'(x) = 4(x).

A: We have to find the general form of the function f if f'x=4 fx. Rewriting the given equation, f'x=4…

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: Consider the function h(x), for which h(2) = -5 and h' (2) = –1. h(x) Find f' (2) for the function…

A: Given function:                                   f(x)=h(x)x   Let's take the derivative of the…

Q: Find a function f(x) such that f'(x) = − 5eª + 3x and ƒ(0) : = f(x) = - 1

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Q: Let f(6) = 54 and f'(6) = 19. Let g(x) = (13+x²)f(x). Calculate the value of g' (6). %3D

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Q: Let S(x) = 4x$ (x' – 6). Evaluate the following specific values of f: (A)(2) = (B) (4) =

A: The objective of the question is evaluate the values.

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: The function f(x)=(x)/(x-1) is discontinous at x=1 because

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

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Q: Find f(x) if f "(x) = x -3/2, f ' (4) = 1  and f(4) = 4.

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Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: Consider the function h(z), for which h(4) = -12 and h'(4) = -7. %3D h(z) Find f'(4) for the…

A: To Determine: find f'4 Given: consider the function h(x) for which h4=-12 and h'4=-7 also…

Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: Let f(1) = 2 and f' (1) = 3. Suppose g(x) = [f(x)5"]. Calculate g' (1).

A:

Q: f(x) 132. Let h (x) = g(x) Find a. h' (1), b. h' (3) , and с. h' (4).

A: Given

Q: If f is the function f (x) = + 4/x, then f' (4)

A: The function is  f(x)=4x+4x

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

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Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

A:

Q: Find f'(1)when f(x) = ln(e*x").

A:

Q: or h' (x):

A: Given that: The equation is h ( x) = g ( x 2 + f ( 3x) ).

Q: Find f′(x) if f(x) = lnx / x2

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Q: Let y= f (x) be a function with f (4)=12 and f(4)= 0.5.

A: We have to find

Q: Find f such that f'(x)=x² +4 and f(0) = 1. f(x) =

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

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: Differentiate the given function: f(x) = In(2r³ – 5æ) 6x² – 5 A f'(x) = 2x3 – 5x 1 ® f'(x) = 2x3 –…

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Q: x2 with g(1) = 2 and g'(1) = 3. Find the value of f"(1). Suppose that f(x) = g(x)

A: Explanation of the answer is as follows