Given the values of f(x), g(x), f'(x) and g'(x) in the table, answer the following questions. x f(x) f'(x) g(x) g'(x) 14 3 -27 26 2 09 38 1 4 5 48 1 3 4 57 -1 2 4 (for example f(4) = 8 and dx at x = 3 dx (f(x)) =3 at x = 1

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: 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: Let y (t) be the solution of the initial value problem y" – 4y' + 5y = e-2t %3D 1 and y' (0) = 17 y…

A: We have to observe the characteristic equation first.

Q: Given the values f(6)=-1, f'(6)=3, g(2)=6, g(2)=5,cfind the value of F(2) based on the function…

A: Given f(6)=-1  f'(6)=3g(2)=6g'(2)=5and    F(x)=f(g(x))

Q: 2. Given f(x)=x-6, determine whether f'(6) exists.

A:

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

A: A detailed solution is given below

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: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

A:

Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

A:

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

A:

Q: 3 (d) h (x) = 3x² – 4x2 + 2 | (e) ƒ (x) = x5 – xª + x³ – x² + x – 1 - | (f) ƒ (x) = x6+x5+x4 – a³ –…

A: Here we have to find  The derivative of the given functions d)…

Q: Consider the following functions. g(x) = x3 – x h(x) = (x3 – x)4 f(x) = 9(x3 – x)4 Find the…

A:

Q: Consider the function f (x) = 25 + 3x² – 7x + 2+4. What is f' (2) ?

A:

Q: If f(x) = 6 + 5x – 5a, find f'(- 3).

A: Topic = Derivative

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

A:

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

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

A: Solve the function

Q: If f(x) = 18z + 9, find f'( – 1).

A:

Q: f (x) = x5, x = 1/2

A: The function is given as fx=x5

Q: f(x) = x' +x² +1 and g(x) = 4 – x²

A:

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: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A: Given