Answer:
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
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