Chapter 1.4, Problem 14E

a. a) Graph the function.

b. b) Draw tangent lines to the graph at point whose x-coordinates are –2, 0, and 1.

c. c) Find $f\text{'}\left(x\right)$ by determining $\underset{x\to 0}{\lim }\frac{f\left(x+h\right)-f\left(x\right)}{h}$.

d. d) Find $f\text{'}\left(-2\right),f\text{'}\left(0,\right)\text{and}f\text{'}\left(1\right)$. These slopes should match those of the lines you drew in part (b).

$f\left(x\right)=-2x^2+3x-2$