Question

The function $\frac{1}{4}$ is not

differentiable at

• A. – 1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (D)

2

Answer 2

$\left( x ^ { 2 } - 3 x + 2 \right) = ( x - 1 ) ( x - 2 ) = + i v e$

When $x < 1$ or $> 2$ –ive when $1 \leq x \leq 2$

Also $\cos | x | = \cos x$ (since $\cos ( - x ) = \cos x$ )

$\therefore$ $f ( x ) = - \left( x ^ { 2 } - 1 \right) \left( x ^ { 2 } - 3 x + 2 \right) + \cos x , \quad 1 \leq x \leq 2$

$\therefore$ .........(i)

Evidently $f ( x )$ is not differentiable at $x = 2$ as $L ^ { \prime } \neq R ^ { \prime }$

Note : For all other values like $x < 0$ $0 \leq x < 1$ $f ( x )$ is same as given by (i).