Question

How do you find the derivative of the function `f(x)=x^2-3x` using `f(x+h)-f(x)/h`?

Answer 1

Know that:

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

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

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

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

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

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

`=2x-3`