Use limits to compute the derivative

Question

Use limits to find the derivative

 

f'(2) if f(x)=4x³

Answer 1

Using limits, you will be performing the limit of the Difference quotient, which is [f(x+h) - f(x)] / h.

There are examples in your Calculus book.

 

f'(x) will turn out to be 12x² and thus f'(2) will be easy to compute.

 

I'm not going through the arduous typing to show intermediate steps.  Hint: it will be necessary for you to know how to expand (x+h)³; the binomial theorem & Pascal's triangle will be used.