Question

Which of the following functions is not differentiable in the domain [-1,1]?

• A. f(x) = x${}^2$
• B. f(x) = x - 1
• C. f(x) = 2
• D. f(x) = maximum (x,-x)

Answer 1

The correct option is D f(x) = maximum (x,-x)

Functions in options (a), (b) and (c) are ploynomail functions and hence differentiable
Let us verify option (d)
f(x) = maximum (x, -x)

f(x) = $\left|x\right|=\{\begin{array}{c}+x,x>0\\ -x,x<0\end{array}$

so LD (Left derivative) = -1

& RD (Right derivative) = +1

$\because LD\ne RD$

The function is not differentiable at x = 0