Chapter 4.8, Problem 10ES

Let $f\left(x\right)=x^3-4x$ .

(a) Find the equation of the secant fine through the points $\left(-2,f\left(-2\right)\right)$ and $\left(1,f\left(1\right)\right)$ .

(b) Show that there is only one point $c$ in the interval $\left(-2,1\right)$ that satisfies the conclusion of the Mean-Value Theorem for the secant line in part (a).

(c) Find the equation of the tangent line to the graph of $f$ at the point $\left(c,f\left(c\right)\right)$ .

(d) Use a graphing utility to generate the secant line in part (a) and the tangent line in part (c) in the same coordinate system, and confirm visually that the two lines seem parallel.