Find the equation of the tangent line to the curve when $x$ has the given value.
-$f(x)=\frac{7}{x-2} ; x=3$
A) $y=\frac{x}{2}-\frac{1}{2}$
B) $y=-7 x-9$
C) $y=\frac{x}{4}+1$
D) $y=-7 x+28$

Question

Quizplus · Accepted Answer

The derivative of $f(x)=\frac{7}{x-2}$ is $f'(x)=-\frac{7}{(x-2)^2}$. At $x=3$, $f'(3)=-7$. The point on the curve is $(3,7)$. The tangent line is $y-7=-7(x-3)$, which simplifies to $y=-7x+28$.

Find the Equation of the Tangent Line to the Curve xxx

Find the Equation of the Tangent Line to the Curve $x$