Question

Given the function h(x) = x^2 + 3x - 1 determine the average rate of change of the function over the interval -7 ≤ x ≤ 5

Answer 1

SOLUTION

The given function is:

$h\mleft(x\mright)=x^2+3x-1$

The given interval is:

$-7≤x≤5$

Rate of change is given as:

$\frac{f(b)-f(a)}{b-a}$

When x=-7 it follows:

$\begin{gathered} h(-7)=(-7)^2+3(-7)-1 \\ h(-7)=27 \end{gathered}$

When x=5 it follows:

$\begin{gathered} h(5)=5^2+3(5)-1 \\ h(5)=39 \end{gathered}$

Therefore the rate of change is:

$\begin{gathered} \frac{h(5)-h(-7)}{5-7} \\ =\frac{39-27}{5-7} \\ =\frac{12}{-2} \\ =-6 \end{gathered}$

Therefore the average rate of change is -6