Mathematics - Quadratic Equation Question with Solution | TestHub

$f(x)=\left({\sin }^2\theta \right)x^3+\frac{1}{2}\sin 2\theta x^2-2{\sin }^2\theta .x-\sin 2\theta$ $f^{\prime }(x)=\left(3{\sin }^2\theta \right)x^2+\sin 2\theta x-2{\sin }^2\theta$

Then $\mathrm{D}>0$ and product of roots < 0

So $f(x)$ has local maxima at some $x\in R^{-}$

and local minima at some $\mathrm{x}\in {\mathrm{R}}^{+}$