HW # 2: Problem Set: Calculus Review

1)Consider the equation: y = ax

a) Take the derivative of y with respect to x. Assume that 'a' is a constant.

2)Consider the equation: y = 7x

a) Graph the equation.

b) Take the derivative of y with respect to x.

c) Find the slope of the equation at x = 2, and point it out on the graph.

3)Consider the equation:y=(1c(1t))bx

a) Take the derivative of y with respect to x. Assume that b, c, and t are constant.

4)Consider the equation: y = bx²

a) Take the derivative of y with respect to x. Assume that 'b' is a constant.

5)Consider the equation: y = 5x³ + 6x² + 8x + 4

a) Take the derivative of y with respect to x.

6)Consider the equation: y = (x 5)² + 4

a) Graph the equation.

b) Take the derivative of y with respect to x.

c) Find the slope of the equation at x = 0, and point it out on the graph.

d) Find the slope of the equation at x = 3, and point it out on the graph.

e) Find the minimum of the graph using the first and second order conditions.

7)Consider the equation: y = ln x

a) Graph the equation.

b) Take the derivative of y with respect to x.

c) Find the slope of the equation at x = 2. What is the slope?

8)Consider the equation: y = e^x

a) Graph the equation.

b) Take the derivative of y with respect to x.

c) Find the slope of the equation at x = 5. What is the slope?

9) Consider the equation: L = L₀ e^nt

a) Take the derivative of L with respect to t to find the growth rate of L.

(Hint: Use the chain rule.)

b) Divide the derivative of L by L to find the growth rate of L in percentage terms.

Note that L₀ and 'n' are constants.