Respuesta :
SOLUTION
The given function is:
[tex]h\mleft(x\mright)=x^2+3x-1[/tex]The given interval is:
[tex]-7≤x≤5[/tex]Rate of change is given as:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]When x=-7 it follows:
[tex]\begin{gathered} h(-7)=(-7)^2+3(-7)-1 \\ h(-7)=27 \end{gathered}[/tex]When x=5 it follows:
[tex]\begin{gathered} h(5)=5^2+3(5)-1 \\ h(5)=39 \end{gathered}[/tex]Therefore the rate of change is:
[tex]\begin{gathered} \frac{h(5)-h(-7)}{5-7} \\ =\frac{39-27}{5-7} \\ =\frac{12}{-2} \\ =-6 \end{gathered}[/tex]Therefore the average rate of change is -6
