Answer
The equation of the tangent is $y=4x+25$.
Work Step by Step
Using the quotient rule: $fâ(x)=(\frac{u(x)}{v(x)})'=\frac{u'(x)v(x)-v'(x)u(x)}{(v(x))^2}$
$u(x)=x; u'(x)=1$
$v(x)=x+4; v'(x)=1$
$f'(x)=\frac{x+4-x}{(x+4)^2}=\frac{4}{(x+4)^2}$.
$f'(-5)=\frac{4}{(-5+4)^2}=4$.
Equation of tangent: $(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-5)=4(x+5)\rightarrow y=4x+25$.
A graphing calculator and a computer algebra system have been used to confirm these results.
