Compute the derivative f'(a) algebraically, using the definition, for the given value of a. f(x)= x-2xˆ3, a=1

Question

myininaya · Answer

$$f'(a)=\lim_{\Delta \rightarrow 0}\frac{f(a+\Delta)-f(a)}{\Delta}$$
So do you know know to find:
$$f(a+\Delta)?$$

anonymous · Answer

i know that my a would be 1 but how do i find $$\Delta$$

myininaya · Answer

that is going to zero....

myininaya · Answer

$$f(a+\Delta)=(a+\Delta)-2(a+\Delta)^3$$
Plug this into our definition and simplify our fraction as much as possible.

myininaya · Answer

Like you would multiply that (a+Delta)^3 thing
And cancel some stuff on top.
If you want to go ahead and replace a with 1, that is cool.

anonymous · Answer

Okay! Thanks a lot :)

myininaya · Answer

Have you simplified the fraction?
After simplifying the fraction you should be able to plug in 0 for delta.