Question

The function $f\left(x\right)={\cos }^{-1}(4x^3-3x)$ is

• A. always differentiable
• B. not differentiable at 2 points only
• C. not continuous at 2 points only
• D. not differentiable at 4 points only

Answer 1

The correct option is D not differentiable at 4 points only

$letf\left(x\right)=y={\cos }^{-1}(4x^3-3x)$ then,


$f\left(x\right)$ has sharp turns at $x=\frac{-1}{2},\frac{1}{2}$ and also vertical tangents at $x=-1,1$.
Therefore $f\left(x\right)$ is not differentiable at $x=-1,\frac{-1}{2},\frac{1}{2},1$.