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Final review question 2

cmarsha4

I keep getting tripped up on this first one. Use the following steps to estimate the derivative of f(x) = 4^x.
(b) Use a little algebra to separate the xs from the hs.
(c) Refer to the following table to help you find your final estimate.

Can anyone show the work they did?

mark

The key algebraic steps are as follows:

\frac{4^{x+h} - 4^x}{h} = \frac{4^{x}4^h - 4^x}{h} = 4^x\frac{4^{h} - 1}{h}.

Note that we’ve now "separated the x terms (4^x) from the h terms (\frac{4^{h} - 1}{h}). You can now use the table to figure out what the limit of the h term is.