Write a difference quotient that best approximates the instantaneous rate of change of g at x=1.

Evaluating 

+h)−f(3)h:

(3+h)2−32h=9+6h+h2−9h

=6+h

You can then estimate the instantaneous rate of change by selecting "small" values of h.

For example, if h=.01, the estimate would be 6.01.

The key idea is that once we've simplified the difference quotient we can let h tend to 0. If h→0, the difference quotient tends to 6, which is the exact instantaneous rate of change at x=3.

Explanation:

Use the difference quotient to estimate the instantaneous rate of change in f(x)=x2 at x=3

#