Question

Find the Derivation of $f\left(x\right)=x^2.atx=0$

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is A

0

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

$\underset{h\to 0}{lim}=\frac{f(x_0+h)-f\left(x\right)}{h}=\underset{h\to 0}{lim}\frac{(x+h{)}^2-x^2}{h}$

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

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

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

$\therefore Derivativeof{x}^{2}at0=0$