Find the equation of the tangent line to the curve when $x$ has the given value.
-$f(x)=x^{2}+11 x-15 ; x=1$
A) $y=-\frac{4 x}{25}+\frac{8}{5}$
B) $y=-39 x-80$
C) $y=\frac{x}{20}+\frac{1}{5}$
D) $y=13 x-16$

Question

Quizplus · Accepted Answer

The derivative of $f(x)$ is $f'(x) = 2x + 11$. At $x = 1$, $f'(1) = 13$, which is the slope of the tangent. The point on the curve is $(1, -3)$. Using the point-slope form, the equation is $y - (-3) = 13(x - 1)$, simplifying to $y = 13x - 16$.

Find the Equation of the Tangent Line to the Curve xxx

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