Question

Find the derivative of x2 – 2 at x = 10

Answer 1

Let f(x) = x2-2. Accordingly,
f'(10)= $\lim_{h\rightarrow 0}$ $\frac{f(10+h)-f(10)}{h}$
= $\lim_{h\rightarrow 0}$ $\frac{[(10+h)^2-2]-(10^2-2)}{h}$
= $\lim_{h\rightarrow 0}$ $\frac{20h+h^2}{h}$
= $\lim_{h\rightarrow 0}$ (20+h)=(20+0)=20
Thus, the derivative of x2 - 2 at x = 10 is 20.