JEE Main 2022 · 27 Jun · Shift 2 · Mathematics Q7

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MathematicsSingle correct+4 / -1Question 7 of 90

If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f(x)=\displaystyle\int_0^{x^2}\frac{t^2-5t+4}{2+e^t}dt$ , then the ordered pair $(m,n)$ is equal to

(3,2)

(2,3)

(2,2)

(3,4)

Answer and worked solution

Official answer: B

Derivative. $f'(x)=\dfrac{2x(x^2-1)(x^2-4)}{2+e^{x^2}}$ , zero at $0,\pm1,\pm2$ .

Signs (left to right): $-,+,-,+,-,+$ across $-2,-1,0,1,2$ . Maxima where $+$ turns to $-$ : $x=\pm1$ . Minima: $x=-2,0,2$ .

So $(m,n)=(2,3)$ .

(B)

Topics:Maxima and minima Leibniz rule

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JEE Main 2022 · 27 Jun · Shift 2, Mathematics question 7