Question

1.Television Viewership

The number of viewers of a television series introduced several years ago is approximated by the function

N(t) = (60 + 2t)^2/3    (1 ≤ t ≤ 26)

where N(t) (measured in millions) denotes the number of weekly viewers of the series at the end of the t th week. Find the rate of increase of the weekly audience at the end of week 6 and at the end of week 11. (Round your answers to one decimal place.)

week 6 million week

week 11 million/week

How many viewers were there in week 6? In week 23?

week 6 million

week 23 million

2. Find an equation of the tangent line to the graph of the function at the given point.

f(x) = (1 − x)(x² − 8)²; (3, −2)

Find

dy

du

,

du

dx

, and

dy

dx

when y and u are defined as follows.

y =

u

      u = 7x − 4x²

dy

du

=

du

dx

=

dy

dx

=

Answer 1