A) No extrema
B) One extremum
C) Two extrema
D) Four extrema
Correct Answer: C
Solution :
\[f(x)=\int_{-10}^{x}{({{t}^{4}}-4){{e}^{-4t}}dt}\] Þ \[{f}'(x)=({{x}^{4}}-4){{e}^{-4x}}\] Now \[{f}'(x)=0\Rightarrow x=\pm \sqrt{2},\,\pm \sqrt{2}\] Now \[{f}''(x)=-\,4({{x}^{4}}-4){{e}^{-4x}}+4{{x}^{3}}{{e}^{-4x}}\] At \[x=\sqrt{2}\] and \[x=-\sqrt{2}\] the given function has extreme value.You need to login to perform this action.
You will be redirected in
3 sec