1. Tardigrade
  2. Question
  3. Mathematics
  4. If m and n respectively are the number of local maximum and local minimum points of the function f ( x )=∫ limits0x2 ( t 2-5 t +4/2+ c t ) dt, then the ordered pair ( m , n ) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f ( x )=\int\limits_{0}^{x^{2}} \frac{ t ^{2}-5 t +4}{2+ c ^{ t }} dt$, then the ordered pair $( m , n )$ is equal to

JEE MainJEE Main 2022Application of Derivatives

Solution:

$m=L \cdot \max$
$N=L \cdot \min$
$f(x)=\int\limits_{0}^{x^{2}} \frac{t^{2}-5 t+4}{2+e^{t}} d t$
$f^{\prime}(x)=\frac{\left(x^{4}-5 x^{2}+4\right) 2 x}{2+e^{x^{2}}}=\frac{2 x\left(x^{2}-1\right)\left(x^{2}-4\right)}{2+e^{x^{2}}}$
$=\frac{2 x(x-1)(x+1)(x-2)(x+2)}{2+e^{x^{2}}}$
image