## Calculus with Applications (10th Edition)

$$y=-28 x+34$$
Given function$$y=x^{4}-5 x^{3}+2$$Putting $x =2$ in $y$ $$y(2)=-22$$ Finding the derivative of the function $$\frac{d y}{d x}=4 x^{3}-15 x^{2}$$ Slope is given by \begin{align*} m&=\frac{d y}{d x}(2)\\ &=4(2)^{3}-15(2)^{2} \\ &=-28 \end{align*} Finding the equation of tangent \begin{align*} y-y_{1}&=m\left(x-x_{1}\right)\\ y-(-22)&=-28(x-2 )\\ y&=-28 x+34 \end{align*}