# Chapter 4 - Calculating the Derivative - 4.1 Techniques for Finding Derivatives - 4.1 Exercises - Page 207: 32

$$y=-31 x+24$$

#### 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*}

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