Mathematics - Application of Derivative Question with Solution | TestHub

Sketch $y=x^{5/3}-5x^{2/3}=x^{2/3}(x-5)$ and $y=K$. For $x>0$ the curve falls from 0 to a minimum and then increases through 0 at $x=5$; for $x<0,y<0$. Hence $y=K$ meets the curve at exactly one positive $x$ only when $K>0$.