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.

Answer 2

Let \( f(x) = x^2 - 2 \)

\( f'(x) = \frac{d(x^2 - 2)}{dx} \)

\( = 2x - 0 \)

\( = 2x \)

So, \( f'(x) = 2x \)

\( f'(10) = 2 \times 10 \)

\( = 20 \)