Question

How do you find f'(x) using the definition of a derivative for `f(x)= 2x^2-x`?

Answer 1

`4x-1`
See the explanation.

Explanation:

`f'(x)=lim_(h->0) (f(x+h)-f(x))/h`

`lim_(h->0) (2(x+h)^2-(x+h)-(2x^2-x))/h=`

`lim_(h->0) (2x^2+4xh+2h^2-x-h-2x^2+x)/h=`
`lim_(h->0) (4xh+2h^2-h)/h=lim_(h->0) (4x+2h-1)=4x-1`