Answer
$p′(4) = 4$
$q′(7)= 3/4$
Work Step by Step
(a) We have that $p(x)=f(x)∗g(x) $ so
$p(4)=f(4)∗g(4)$
$p′(4)=f(4)∗g′(4)+g(4)∗f′(4)$
watching the graph:
$f(4)= 1$
$g′(4)=0$
$g(4)=8$
$f′(4)=1/2$
So
$p′(4) = 1(0)+8(1/2) = 0+4 = 4$
(b) We have that $q(x)=f(x)/g(x)$ so
$q(7)=f(7)/g(7)$
$q′(7)=\frac{g(7)∗f′(7)−f(7)∗g′(7)}{[g(7)]^2}$
watching the graph:
$g(7)= 4$
$f′(7)= 2$
$f(7)= 4$
$g′(7)=-1$
So
$q′(7)=\frac{4(2)−4(-1)}{16}= \frac{8+4}{16} = 3/4$
