if f(x)=x^2+3x-2, then find f(3) and
f(x+h) and f(x+h)-f(x)/x.
f(x)=x^2+3x-2
f(3)=3^2+3*3-2=16
f(x+h)=(x+h)^2+3(x+h)-2
=x^2+(2*h+3)*x+h^2+3*h-2
Therefore
(f(x+h)-f(x))/h
=(x^2+(2*h+3)*x+h^2+3*h-2 - (x^2+3x-2))/h
= 2*x+h+3
Note that (f(x+h)-f(x))/h evaluates to f'(x) when Lim h→0.
Note: Please check the expression f(x+h)-f(x)/x, I believe there should be implicit parentheses on the numerator and the denominator should be h, i.e.
expression = (f(x+h)-f(x))/h
If it is otherwise, please post.