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

1 Answer
Apr 20, 2015

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