What is the instantaneous rate of change

Question

Solve the following:

Q1. Differentiate

a. Y = 3x + PI^3

b. Y = 1 / (x-3)^3

c. y = (x^4 - x)^3 (3x + 2)^4

d. Y = (1 + x - x^3)^4

Q2. Compute the following limits.

a. lim_x→∞[(x-2)/(x^2+2)]

b. lim_x→∞[(3x^5- 6x^4+ 2x-6)/(7x^5- 2x^2+ 10,000)]

Q3. Use limits to compute f"(3) where f (x) = x^2 - 2x +3.

Q4. a. What is the average rate of change of f(x) given f(x) = -6/x from [1,2] and [1,4].

b. What is the instantaneous rate of change of f(x) when x = 1.

Q5. Write the equation of the tangent line to the curve y = x^3 - 2x^2 +5 at x = 2.