1. Find f(x) if f'(x) = x/x and f(1) = 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: 8. Find f'(x) for the function f (x) = (5x² + 3)4

A: ddxfxn=nfxn-1f'x

Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx > 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

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

A:

Q: Let f(x)=√1+4x f'(3)

A: We know that the derivative of x^n=nx^(n-1)

Q: Let f(7) = -7 and f'(7) = 6. What is gʻ(7) it g(x) = 4+f(x), Enter the answer as a fraction or…

A:

Q: 3. Find f'(x) for f(x) = 3x-4 2x+3

A:

Q: Suppose f(x) √₂+² = √1+tdt 2x find f'(1).

A:

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

A:

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: then compute f'(4). f(x) = x³ + 2x² x√x

A:

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

A:

Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Given: fx=ex2, x=0, 4, E=0.0002 To find: n To find: Approximate integral.

Q: Find a function f(x) such that f'(x) = 9x² +2 and f(0) = 1 f(x) =

A:

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

A:

Q: Let c =8 If f (x) = ecsin(). Find f' (0)

A: Given c=8and f(x)=ec.sin(x)⇒f(x)=e8sin(x)

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

A: We have to find domain

Q: = 2. Find f(x) if f'(x) = 7//1 – x2 and f f(x) |

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(x) (1)? = 2 x² + 3x x+1 " then what is

A: Given: f(x)=x2+3xx+1

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

A:

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

A:

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

A: Solve the function

Q: 2 7. Evaluate f' (-1) for f(x) =- x X3

A:

Q: Find F'(0) if F'(x)= (1+x) (2+ x)² (3 + x)³ (4 + x)+.

A: Solve the given problem.

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

A: We have to find

Q: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

Q: If f(x)- Vu² - 1 du, then what is f'(3)?

A: I am going to solve the given problem by using some simple calculus to get the required result.

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

A:

Q: 4. Find F'(8) if F (x) = x

A:

Q: If f(x) = (2² + 5x + 3)“, then s'(#) - [ f'(x) -

A: To find the derivative of the given function, we need to use chain rule of differentiation and some…