Reference no: EM131577829

MATH 1325 CALCULUS FOR BUSINESS AND SOCIAL SCIENCES

1. Find the derivative of each function. Be sure to simplify your answer.

a) y = (2x³ + 9x)⁵

b) y = 8√(4x² + 7)

c) y = 0.2e^5x

d) y = 3·4^{x^2+2}

e) y = log₅(3x² - 7x)

f) y = ln(2x + 5)

2. Find the derivative of each function. Be sure to simplify your answer.

a) y = x²+4x/(3x³+2)⁴

b) y = x²e^-2x

c) y = (3x+1)ln(x-1)

d) y = x³-1/ln x

e) y = e^x/2x+1

f) y = log₃(x²+2x)⁴

3. Suppose that the total revenue from the sale of x televisions is given by R(x) = 1000(1 - x/500)².

a) Find the marginal revenue function, R'(x).

b) Find and interpret R'(400), R'(500), and R'(600).