Use the difference quotient to estimate the instantaneous rate of change in f(x)=#x^2# at x=3?

1 Answer
Jan 26, 2018

See explanation.

Explanation:

Evaluating #(f(3+h)-f(3))/h#:

#((3+h)^2-3^2)/h = (9+6h+h^2-9)/h#

#=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 to 0#, the difference quotient tends to 6, which is the exact instantaneous rate of change at #x=3#.