Find the Derivation of $f (x) = x^{2} . a t x = 0$

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Solution

The correct option is A
0

Clearly f(x) is continuous at $x^{2}$ and x write no sharp edges at x=0

$lim h \to 0 = \frac{f (x_{0} + h) - f (x)}{h} = lim h \to 0 \frac{(x + h)^{2} - x^{2}}{h}$

$lim h \to 0 \frac{x^{2} + 2 x h + h^{2} - x^{2}}{h}$

$lim h \to 0 = \frac{h (2 x + h)}{h} = lim h \to 0 (2 x + h) = 2 x$

at $x \to 0 = lim h \to 0 (2 x + h) = 0$

$∴ D e r i v a t i v e o f x^{2} a t 0 = 0$

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