Chapter 4 - Calculating the Derivative - 4.1 Techniques for Finding Derivatives - 4.1 Exercises - Page 207: 31

$$ y=-28 x+34 $$

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*}