Question

How do you use the definition to find the derivative of `3x^2-5x+2`?

Answer 1

`6x-5`

Explanation:

Let `f(x)=3x^2-5x+2`

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

`=lim_(h->0)((3(x+h)^2-5(x+h)+2)-(3x^2-5x+2))/h`

`=lim_(h->0)(3x^2+6xh+3h^2-5x-5h+2-3x^2+5x-2)/h`

`=lim_(h->0)(h(6x+3h-5))/h`

`=6x-5`