Question

Let

f(x) = x³ − 2x².

Find the point(s) on the graph of f where the tangent line is horizontal.

(x, y) = 0	(smaller x-value)
(x, y) =	(larger x-value)

B)

A straight line perpendicular to and passing through the point of tangency of the tangent line is called the normal to the curve. Find an equation of the tangent line and the normal to the curve y = x³ - 3x + 1 at the point (3, 19).

tangent line	y =
normal line	y =

C) As use of the Internet grows, so does the number of consumers who shop online. The expected number of online buyers, as a percent of net users, is represented by the following function where t is measured in years, with t = 1 corresponding to the beginning of 2002.† (Round your answers to one decimal place.)

P(t) = 53t ^0.12      (1  t  7)

(a) How many online buyers, as a percent of net users, are there expected to be at the beginning of 2008?
%

(b) How fast is the number of online buyers, as a percent of net users, expected to be changing at the beginning of 2008?
%/yr

Answer 1