Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4). y (6, 6) 6. 5 (6, 5) 40 (2, 4) f 1 X 1 4 5 6. 7 (a) r'(1) = (b) s'(4) = Need Help? Read It 3. 2.

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: If f(t) = (t + 7t + 3) (5t² + 6), find ƒ'(t). Find f'(5).

A: Given : ft = t2 + 7t + 35t2 + 6

Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

A:

Q: Find a function f(x) such that ƒ'(x) f(x) = – 6x² – 1 and ƒ(0) = 5

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Q: If f(t) = (t + 7t + 3) (5t? + 4), find f'(t). %3D Find f'(1).

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Q: What is the domian of f'(x)?

A:

Q: If f(t) = (t² + 6t + 7) (7t² + 4), find ƒ'(t). Find f'(2).

A: INTRODUCTION A function's differentiation can be used to display the rate of change of a function at…

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

A: Given

Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

A: given function to find the derivative

Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: If f(x, y) = (5x- y²) (a) f(1,4) find the following.

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Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: Provide the table of signs for both f' and ff'.

A: Given function is fx = x+334x-12 = x4 +12x-1+16x-12 +114. Also, given that f'x = x-9x+324x-13    and…

Q: Let F(æ) = f(f(æ)) and G(x) = (F(x))² . You also know that f(3) = 10, f(10) = 2, f'(10) = 3, f'(3) =…

A:

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: Find f such that f'(x) = f(x)= f(16) = 21.

A: Topic:- application of integration

Q: If F(x) = f(g(x)),

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Q: If f(t) = (t + 3t + 6) (4t² + 3), find f (t). Find f'(3).

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Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

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Q: If f(4) = 3 and f'(x) 2 3 for 4 s xs 9, how small can f(9) possibly be? (9) 2

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Q: F:(- 2, 2] → R, F(x) = [, (t- 3)(f² + 1) dt

A: Given, Fx = ∫-2x2t - 3t2 + 1 dtFx = ∫-2x2t3 - 3t2 + t - 3 dtFx = t44 - 3t33 + t22 - 3t-2x2Fx = x44 -…