#### Answer

$$y=-31 x+24$$

#### Work Step by Step

Since $$y=-3 x^{5}-8 x^{3}+4 x^{2},\ \ \ x=1 $$
Then $y(1)=-7$
Finding the derivative of the function$$
\frac{d y}{d x}=-18 x^{4}-24 x^{2}+8 x
$$
Then slope given by
\begin{align*}
m&=\dfrac{dy}{dx}\bigg|_{1}\\
&=-18(1)^{4}-24(1)^{2}+8(1)\\
&=-31
\end{align*}
Hence the equation of tangent given by
\begin{align*}y-y_{1}&=m\left(x-x_{1}\right) \\
y-(-7)&=-31(x-1)\\
y& = -31 x+24
\end{align*}