2. Suppose the mgf of X is (a) Pr(X ≤) Mx(t)=¹, t#0 t = 0. (b) E(X²)

Q: f'(x) = V= and f(1) = 3- I|

A: Explanation of the answer is as follows

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

A:

Q: 5) Suppose the function C(1), where trepresents the number of months from January 1, 2020,…

A: Given, C(t)  represents the energy cost to a manufacturing company, where t is the number of months…

Q: Consider the function f(t, p) 3 (pе' +1—р)". a. Find an expression for f(t, p) and evaluate that…

A: Given that:f(t, p)=(pet+1-p)n

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: 1. For what value of the number k does the function f(x) = (1 + kr + ²)e have f'(0) = 57 (A) 0 (B) 2…

A: f(x)=

Q: Find an expression for f (t, p) and evaluate that expression when t = 0. Find an expression for f(t,…

A:

Q: O X 3. Find f'(x) when f(x) = √16x²

A:

Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: If f(x) = 5x4 - 2e, find: ƒ'(x) = f'(3)= f''(x) = f''(3) =

A:

Q: Find the most general function F such that F'(x) – 14. x5 || - F(x) = Σ

A:

Q: (d) Let h(x) g(f(x)). Use the figure below to find h'(1) or state why the derivative does not exist.…

A:

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

A:

Q: Let f(x) = t° dt. Evaluate the following. f'(x) = f'(5)

A:

Q: 6. Suppose we don't know the formula for the function y = f(x), but we know that f(2)=-3 and that x²…

A: Given: f'(x) =  x2 / ( √1+x2 ) f(2) = -3

Q: Suppose C(x), R(x), and P(x) are the total cost, revenue, and profit of producing items. Match the…

A: The cost function, revenue function, and profit function are respectively :C(x), R(x), and…

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: Compute f'(a) algebraically for the given value of a. f (x) 2x – a2; a = -1 limp 0 (4 – h) = 0 limp…

A: The function is given by f(x) = 2x-x2; a =-1 To evaluate : f'(a) Formula Used : f'(a) = limh→0f(a+h)…

Q: Suppose F(x) is between 4 and 8 for x in [3,12]. What is the largest that · 12 L" F (x) dx can be?

A: given that function F(x) between 4 and 8 for x in [3, 12] we have to find the largest value of…

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

A:

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: Let f(x) = 2x² – 12x + 3. For what x-value isf' (x) = 0? x =

A: To find: The values of x at which f'(x)=0. Given information: The function is f(x)=2x2-12x+3.…

Q: =- Determine the values of c and d for f(x) = fƒ (7) = 0. For what value(s) of x is f(x) increasing?…

A:

Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.