If f(x) = x² then find \(\frac{f(2+h) – f(2)}{h}\)

Solution

Given

f(x) = x²

We have to find \(\frac{f(2+h) – f(2)}{h}\) so,

f(2+h) = (2+h)² = 4 + 4h + h²

f(2) = 4

Now,

\( = \frac{f(2+h) – f(2)}{h}\)

\(= \frac{4 + 4h + h^2 – 4}{h} \)

\(= \frac{h(4 + h)}{h} \)

= 4 + h