The correct option is D Has one point of local minima
We have,
f(x)=x13(x−1)=x43−x13⇒f′(x)=43x13−13(1x23) =13x23[4x−1]
For stationary points f′(x)=0
⇒x=14 is the only stationary point
and x=0 and x=14 are the two critical point,
∵ at x=0 function has a vertical tangent
Now, f′(x) changes its sign from negative to positive as it crosses x=14, from left to right, which is point of minima.