Assignment:
Q1. Use the Product Rule to find the derivatives of the following functions:
a. f(X) = (1- X^2)*(1+100X)
b. f(X) = (5X + X^-1)*(3X + X^2)
c. f(X) = (X^.5)*(1-X)
d. f(X) = (X^3 + X^4)*(30 + X^2)
Q2. Use the Chain Rule to find the derivatives of the following functions:
a. f(X) = (1- X^2)^5
b. f(X) = (5X + X^-1)^-1
c. f(X) =(1-X)^2
d. f(X) = (X^3 + X^4)^3
Q3. Use the Quotient Rule to find the derivatives of the following functions:
a. f(X) = 100/X^4
b. f(X) = 1/(5X + X^2)
c. f(X) =5/(1-X)
Q4. For each of the following functions find the 1) first and second derivative, 2) explain whether or not the function has a maximum or a minimum, and how you reached that conclusion, and 3) the value of the maximum or minimum
a. f(X) = 5X^2 - 2X
b. f(X) = 1000X - X^2
c. f(X) = 8X^3 - 4X^2
Provide complete and step by step solution for the question and show calculations and use formulas.