Math $2413$: Worksheet $7$

Page $2$ of $3$

c$.$

Hor the following exercises, assume that $f(x)$ and $g(x)$ are both differentiable functions with values as given in the following table. Use the table to calculate the following derivatives.

$\backslash$table$[[x,1,2,3],[f(x),2,4,-3],[g(x),-2,6,5],[f(x),3,-1,8],[g^{\text{'}}(x),-4,-5,7]]$

i$.$ Find $h^{\text{'}}(2)$ if $h(x)=xf(x)+5g(x).$ First take the derivative of $h(x)$; then evaluate the functions at $x=2$ using the table. Show all steps.

$f(2)=4,y(2)=6$

$f^{\text{'}}(2)=-1,y^{\text{'}}(2)=-5$

$w(x)=xf(x)+5g(x),x=2$

$3$i$.$ Find $h^{\text{'}}(3)$ if $h(x)=\frac{g(x)}{f(x)}.$ Show all steps.

$g(3)=5,f(3)=-3$

$g^{\text{'}}(2)=T,f^{\text{'}}(3)=8$

$(-3)(7)-(8)(5)$

$\{\begin{array}{c}\text{:}f(3)=-3\\ \frac{(-3)|7|-(8)(5)}{f^{\text{'}}(3)}=8\frac{(-3{)}^2}{\frac{-21-40}{4}\frac{-61}{9}}\end{array}$