If the function f(x)=(1)/(|x|), & |x| 2 ax^2+2b, & |x|is differentiable on R, then

Question

If the function

$f(x)=\frac{1}{|x|}, \& |x|\geqslant 2  \  a{x}^{2}+2b, \& |x|is differentiable on $R$, then $

Accepted Answer

$f(x) $$frac{1}{x};x\ge 2  \  {ax}^{2}+2b;-2Continuous at $x=2\, \Rightarrow \frac{1}{2}=\frac{a}{4}+2b$$$

Continuous at $x=-2\, \Rightarrow \frac{1}{2}=\frac{a}{4}+2b$

Since, it is differentiable at $x=2$

$-\frac{1}{{x}\^{2}}=2ax$

Differentiable at $

Solutions · 1