Math 103. Homework 10. Due 5/8/02

1. Determine the intervals where the function

f(x)=x2 e-x

is increasing and the intervals where it is decreasing.

2. Determine the intervals of concavity and inflection points for the function

f(x) = x2 lnx

3. Use logarithmic differentiation to find an equation for the tangent line to the graph of

f(x) = xlnx

at the point (e,e).

4. Find the present value of $119,346 due in 4 yr at an interest rate of 10%/year compounded continuously.

5. A hotel was purchased by a conglomerate for $4.5 million and sold 5 years later for $8.2 million. Find the annual rate of return, compounded continuously.

Suggested Exercises Section 5.1.- 1-29 Section 5.2.- 1-42 Section 5.3.- 1-9, 12, 16, 19, 21, 24, 27, 29. Section 5.4.- 1-44. 50, 52, 54, 56, 57, 58, 59. Section 5.5.- 1-56