UPSC NDA Math Model Paper 6

Observe the graph of the function f(x) = |x|.
At x = 1 the curve is smooth and thus the function is differentiable at x = 1.
On the other hand the function is not differentiable at x = 0 as it has a corner at x = 0.
Observe the graph of the function f(x)=ex
.At x = 0 the curve is smooth so it is differentiable at x = 0.
Thus only the second statement is true.