Question

Let f(x)=4-x^2,


find ( f(x+h)-f(x) ) / h and simplify

Answer 1

If
`f(x)=4-x^2`, then

`f(x+h)=4-(x+h)^2=4-(x^2+2xh+h^2)=4-x^2-2xh-h^2`

So

`\frac{f(x+h)-f(x)}h=\frac{(4-x^2-2xh-h^2)-(4-x^2)}h=-\frac{2xh+h^2}h`

Then for
`h\\eq0`, we can cancel common terms:

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