How do you do this: Use the limit definition to compute the derivative of the function at x = 5.f(x) = 4x−1
f '(5) =

Question

How do you do this: Use the limit definition to compute the derivative of the function at x = 5.f(x) = 4x−1
f '(5) =

anonymous · Answer

Can you help me on a problem?

anonymous · Answer

The limit definition of a derivative is $$f'(x) = \lim_{h \rightarrow 0} \frac {f(x+h) - f(x)}{h}$$  In order to solve your equation, you need to substitute your function into the equation above and simplify.

anonymous · Answer

When I tried that I continually get zero on the bottom. Also do you know what the tan line to the graph would be at x=-1

kirbykirby · Answer

Substitute what you have into the definition, and the h will disappear on the bottom :) 

$$f'(x) = \lim_{h \rightarrow 0} \frac {\color{red}{f(x+h)} - \color{blue}{f(x)}}{h}=\lim_{h \rightarrow 0} \frac {\color{red}{4(x+h)-1} - [\color{blue}{4x-1}]}{h}$$
Expand the numerator, and all should be good :o