A function is defined as $$f(x)=[x](x^2-25)^n((x^2+3)(x^2+3x+4)^3)^m, m,n\in \mathbb N$$
Where [$x$] represents the the function defined as [$x$]="the greatest integer less than or equal to $x$".
Its also known that $f(x)$ attains minimum value at $x=5$. We have to find the value of $m$ and $n$ with this information.
I tried differentiating and putting the value of $x=5$, but all terms becomes zero. This was a multiple choice question and the options were:
A) $m=10,n=5$ B)$m=5,n=10$
C)$m=20,n=5$ D)$m=10,n=3$
I cannot find any method to solve this question and even taking the first and second derivative at $x=5$ takes much time, while the average time allotted per question is about two minutes.