Chapter 2.2, Problem 3ES

(a) If you are given an equation for the tangent line at the point $\left(a,f\left(a\right)\right)$ on a curve $y=f\left(x\right)$ , how would you go about finding $f^{\prime }\left(a\right)$ ?

(b) Given that the tangent line to the graph of $y=f\left(x\right)$ at the point $\left(2,5\right)$ has the equation $y=3x-1$ , find $f^{\prime }\left(2\right)$ .

(c) For the function $y=f\left(x\right)$ in part (b), what is the instantaneous rate of change of $y$ with respect to $x$ at $x=2$ ?