The function $f(x)=\frac{x^4}{4}-\frac{x^2}{2}$ has

2 points of local maxima 2 points of local minima and one point of local maxima 1 point of local minima and 2 points of local maximum 1 point of local maxima and 1 point of local minima

2 points of local minima and one point of local maxima

The correct answer is Option (2) → 2 points of local minima and one point of local maxima $f(x)=\frac{x^4}{4}-\frac{x^2}{2}$ $f'(x)=x^3-x=0$ $⇒x(x^2-1)=0$ $x=0,1,-1$ Using wavy curve method Points of local minima ⇒ -1, 1 Points of local maxima ⇒ 0