Answer
$y=-24x-23.$
Work Step by Step
Using the Chain Rule:
$u=4x^3+3$; $\dfrac{du}{dx}=12x^2$
$\dfrac{dy}{du}=2u$
$\dfrac{dy}{dx}=\dfrac{dy}{du}\times\dfrac{du}{dx}=24x^2(4x^3+3)=96x^5+72x^2.$
$y'$ evaluated at $(-1, 1)\rightarrow y'=96(-1)^5+72(-1)^2=-24.$
Equation of tangent:
$(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-1)=-24(x+1)\rightarrow y=-24x-23.$
A graphing calculator and a computer algebra system have been used to confirm these results.
