Question

Let $g\left(x\right)=max\{\frac{x^2}{2},2x^2-3x+\frac{3}{2}\}$ then

• A. $g\left(x\right)$ is continuous but not differentiable $\forall x\in R$
• B. $g\left(x\right)$ is discontinuous
• C. $g\left(x\right)$ is non-differentiable at one point
• D. $g\left(x\right)$ is continuous and differentiable $\forall x\in R$

Answer 1

The correct option is D $g\left(x\right)$ is continuous and differentiable $\forall x\in R$

$\frac{x^2}{2}=2x^2-3x+\frac{3}{2}$

$3x^2-6x+3=0\Rightarrow x^2-2x+1=0\Rightarrow (x-1{)}^2=0$

$\therefore x=1$

These two curves touch each other.



So $g\left(x\right)$ is continuous and differentiable.