Let h(x)=min{x, x2}, ∀ x∈R, then -h(x) is not differentiable at two values of xh(x) is differentiable ∀ x∈Rh′(x)>0, ∀ x>1None of these

Let h(x)=min{x, x2}, ∀ x∈R, then -h(x) is not differentiable at two values of xh(x) is differentiable ∀ x∈Rh′(x)>0, ∀ x>1None of these

Define g : R → R byg(x) =(x2 cos(1/x) if x̸ = 0,0 if x = 0.Show that g is differentiable at x for every x ∈ R

Definef (x) =(x2 if x is rational,0 if x is irrational.Show that f is differentiable at 0 and f ′(0) = 0

Let the area of the region {(x,y):0≤x≤3,0≤y≤ min{x2+2,2x+2}} be A. Then 12 A is equal to ______

Determine whether following function is differentiable at the given point.f(x) = cos(x)x2 + 1, x = 0