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: If f"(x) = t"(x) for 0 < x < 1, then f(x) − t(x) for 0 < x < 1.

A: It is given that f''(t)=t''(x) for 0<x<1. It is known that derivative and integration are…

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: find the function f(x) if f'(x)=(2/1+x2)+(5/7)x5/7 and f(0)=2

A: Given, f'(x)=(2/(1+x2))+(5/7)x5/7

Q: Differentiate the following function. f(x) = (x+2) e-6x +1 f'(x) = (Type your answer in factored…

A:

Q: graph F(X), Determine f'(x) then graph T] f(x) = 1 + x + x

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Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

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: Find f such that f'(x) = f(1) = 21. f(x) =O

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

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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: 7 x + 2 Let f(x) = x4 . x + 5 f'(x) = %3D

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: e8(x) and g(x) 43. Find f'(2) if f(x)

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Q: For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

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

A: The function is  f(x)=4x+4x

Q: Let f(x) and g(x) be functions whose graphs are shown below. Which of the following statements…

A: We are asked about the derivative of the function h given a graph of the functions f and g. Note…

Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

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

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Q: a) If f (x) = 12x, find f' (27). %3D

A: Solve the function

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

A:

Q: Find f(2) if f (x) = e"

A: given equation f(x)=ex

Q: Find f′(x) if f(x) = lnx / x2

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Q: Consider the function f(x)=eXx. Select all that apply. Select 3 correct answer(s) f(0) is positive.…

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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: 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

Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

A: