Get Answers to all your Questions

header-bg

If $\mathrm{m\: and \: n}$ respectively are the number of local maximum and local minimum points of the function $\mathrm{f(x)=\int_{0}^{x^{2}} \frac{t^{2}-5 t+4}{2+e^{t}} d t}$ , then the ordered pair $\mathrm{\left ( m,n \right )}$ is
Option: 1
$\mathrm{\left ( 3,2 \right )}$

Option: 2
$\mathrm{\left ( 2,3 \right )}$

Option: 3
$\mathrm{\left ( 2,2 \right )}$

Option: 4
$\mathrm{\left ( 3,4 \right )}$

Answers (1)

best_answer

$\mathrm{f^{\prime}(a) =\frac{2 x-\left(\left(x^{2}\right)^{2}-5 x^{2}+4\right)}{2+e^{x^{2}}}} \\$

$\mathrm{=\frac{2 x\left[\left(x^{2}-1\right)\left(x^{2}-4\right)\right]}{2+e^{x^{2}}}}$

$\mathrm{=\frac{2(x+2)(x+1) x(x-1)(x-2)}{2+e^{x^{2}}}}$

So $\mathrm{\{-2,0,2\}}$ are poits of Minima $\mathrm{\Rightarrow n=3 }$

and $\mathrm{\{-1,1\}}$ are poits is Maxixma $\mathrm{\Rightarrow m=2 }$

$\mathrm{(m,n)= (2,3) }$

Hence the correct answer is option 2

Posted by

Deependra Verma

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

5 g of Na₂SO₄ was dissolved in x g of H₂O. The change in freezing point was found to be 3.82⁰C. If Na₂SO₄ is 81.5% ionised, the value of x (K

A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The leftover organic phase was extracted with d

Trending Articles/News

anam-khan

In JEE Main 2025 April 3 shift 2, chemistry takes U-turn to be tougher than physics, mathematics

anam-khan

JEE Main 2025 April 3 Exam Analysis 2025: Shift 1 paper easy to moderate; chemistry section ‘easiest’

anam-khan

JEE Mains 2025 admit card out for April 7, 8, 9 exams; download on jeemain.nta.nic.in

Latest Question