Chapter 11.1, Problem 97E

GE Net Income 2009-2013 The annual net income of General Electric for the period 2009-2013 could be approximated by

$P\left(t\right)=-0.39t^2\text{+5}\text{.2}t-\text{4}\text{.1 billion dollars }\left(4\le t\le 8\right)$

Where t is time in years since 2005.

GE net income ($ billions)

a. Compute $P\text{'}\left(t\right)$. How fast was GE’s annual net income changing in 2011? (Be careful to give correct units of measurement.)

b. According to the model, GE’s annual net income

(A) increased at a faster and faster rate

(B) increased at a slower and slower rate

(C) decreased at a faster and faster rate

(D) decreased at a slower and slower rate during the first 2 years shown (the interval $\left[4,6\right]$

). Justify your answer in two ways: geometrically, reasoning entirely from the graph, and algebraically, reasoning from the derivative of P. [HINT: See Example 4.]