From the Indian Joint Entrance Examination – Main:
Find the number of minimizers of the following sextic univariate polynomial $$f(x) = 10x^6 - 24x^5 + 15x^4 - 40x^2 + 108$$
I know the general method for cubic polynomials is finding roots of $f'(x)$ and checking for sign of $f''(x)$ at those points, but I am not able to solve for degree $6$.