Question

How do you find the f'(x) using the formal definition of a derivative if `f(x)= 2x^2 - 3x+4`?

Answer 1

`f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h`

For `f(x) = 2x^2-3x+4`
this becomes

`f'(x)`

`= lim_(hrarr0)((2(x+h)^2 -3(x+h) +4) - (2x^2 -3x +4))/h`

`= lim_(hrarr0) (4xh + h^2-3h)/h`

`=lim_(hrarr0) (4x +h -3)`

`= 4x-3`