Chapter 4.1, Problem 98E

GE Net Income 2007–2011 The annual net income of General Electric for the period 2007–2011 could be 8 approximated by

$P\left(t\right)=1.6t^2-\text{15}t+\text{46 billion dollars }\left(2\le t\le 6\right)$,

Where t is time in year since 2005.

GE net income ($ billions)

a. Compute $P\text{'}\left(t\right)$. How fast was GE’s annual net income changing in 2008? (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 $\left[2,4\right]$

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