Math 103. Homework 8. Due 4/17/02

1. [33, p. 293] Find the intervals where the function

f(x)= x2-1 x

is decreasing and the intervals where it is increasing.

2. Find the intervals where the function

f(x) = 2 1+x2

is concave upward and the intervals where it is concave downward.

3. Exercises 44-45-46-47, p. 294. (These 4 exercises form part of a single one.)

4. [58, p. 294] Find the relative maxima and relative minima, if any, of the function f(x)=x⁴-6x²+8x-16.

5. [78, p. 317] The total annual revenue R of the Miramar Resorts Hotel is related to the amount of money x the hotel spends in advertising its services by the function

R(x) = -0.003 x3 +1.35 x2 +2x +8000       (0 £ x £ 400)

where both R and x are measured in thousands of dollars. Find the inflection point of R and discuss its significance.

Suggested Exercises Section 4.1.- 18, 29, 61, 67, 73, 80. Section 4.2.- 27, 45, 61, 72, 77, 79. Section 4.3.- 1-10, 12-20. Section 4.4.- 19, 20, 44, 49, 55.