Let the function f(x)=(x^2-1)|x^2-a x+2|+ |x| be not differentiable at the two points x==2…

Question

Let the function $f(x)=\left(x^2-1\right)\left|x^2-a x+2\right|+\cos |x|$ be not differentiable at the two points $x=\alpha=2$ and $x=\beta$. Then the distance of the point $(\alpha, \beta)$ from the line $12 x+5 y+10=0$ is equal to :

Accepted Answer

$\cos |\mathrm{x}|$ is always differentiable

$\therefore$ we have to check only for $\left|\mathrm{x}^2-\mathrm{ax}+2\right|$

$\therefore$ Not differentiable at

$x^2-a x+2=0$

One root is given, $\alpha=2$

$$\begin{aligned}
\therefore \quad 4 & -2 a+2=0 \
& a=3
\end{aligned}$$

$\therefore$ other root $\beta=1$

but for $x=1 f(x)$ is differentiable

(Drop)

Solutions · 1