Find the following using the table below. 1 2 3 4 f(x)| 3 2 4 1 f'(x) | 1 4 3 2 9(x) 3 2 1 4 g'(x) | 31 4 2 E (x),6 h'(2) if h(x) = f(9(x)) %3D

Q: Below is the graph of f"(x). For what values of x is f(x) concave up? 1S (x) + + -8 -7 -6 -4 -3 -2…

A: Topic:- Functions

Q: Use the given information to find f '(9). f(x) = 3g(x) + h(x) g(9) = -4 and g'(9) = -1 h(9) = -5 and…

A: Given: fx=3gx+hx.We need to find f'9.

Q: Differentiate the following with respect to x: f(x) = x³In (x)

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Q: How are the functions f and g given by f (x) = (1.05)ª and g (x) = eº.05z similar? How are they…

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Q: Use the guidelines from section 4.5 to graph the function f(x) = x2/3 (6 – x)/3 For your…

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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: Determine h(1) and h'(1). h(x) = [f (x)]2

A: The function h(x) is a composite function since its input is another function f(x). Now h(x)=[f(x)]2…

Q: Use the table below to find h'(-1) for h (x) = f (g (x)). I()9() lO() 1/2 0. -2 -3 1. -1 -1 -2 -2 -2…

A: Given that hx =fgxTo find : h'-1Solution hx =fgxh'x =f'gx×g'xx=-1h'-1 =f'g-1×g'-1h'-1 =f'-2×2h'-1…

Q: f(x) = x². Simplify f(x) = f(a) x-a , xa.

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Q: Find f'(1) if f(x) = √√√x + )=√x+ +2

A: We are given,

Q: 2 If f'(x) = 3x2 - and X f(1) = 0, find f (x)

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Q: let (X)> and fre)=2, f ( X) is

A: Answer and explanation is given below

Q: Determine h(1) and h'(1). h(x) = f (x) / g (x)

A: Value of the function is , the value of combined function, when variable is replaced with that…

Q: A. Find the derivative of each function. 1. f(x) = 26 2. g(x) = -9 3. f(x) = x+7 4. y = 4-2x 5. f(x)…

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Q: Let f and g be functions that satisfy f'(2) = -6 and g'(2) = 9. Find h'(2) for each function h given…

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Q: Use the following information to determine an equation for f(x): f"(x)= 6, f '(0) = 4, and f(0) =-5.

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Q: 1. Differentiate the following f(x) = (2x) (e4x)

A: f(x)= 2xe4x Find f'(x)

Q: The graphs of the functions are shown in the Let h(x) = f(x) g(x) and k(x) = f(x) g(x) & figure. ,…

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Q: f F(x)=ex , find f(ln(2))

A: fx=exfind f(ln(2)) Formula used elnea=a

Q: f(x) = x' +x² +1 and g(x) = 4 – x²

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Q: (a) Let h(x) = f(x)/g(x). Find h'(1). (b) Let h(x) = g(f(x)). Find h'(-1).

A: Definition used -           Quotient rule of derivative -…

Q: Given f(x)=x+(1/x).   Find f(a).

A: Given, The function is f(x)=x+(1/x).

Q: Let f (x) = - x² – 3. Find and simplify ƒ' (x) and ƒ" (x). x5 f" f'(x) = A = -3 B C = || f" (x) D E…

A: Given Function f( x ) as follows

Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

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Q: Let f and g be the functions defined for x > 0 by f(x) = (Væ)* and g(x) = (Vx)** Which function is…

A: According to the given information, Consider the function f and g defined as:

Q: Find the general form of f if f'(x) = 5f(x).

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