Question

Find the difference quotient of f(x)=x^2-3; that is, find [f(x+h)-f(x)]/h, h =/= 0

Answer 1

`\frac{f(x+h)-f(x)}h=\frac{((x+h)^2-3)-(x^2-3)}h=\frac{x^2+2xh+h^2-3-x^2+3}h=\frac{2xh+h^2}h=2x+h`