MHT CET · Maths · Application of Derivatives
If \(\mathrm{f}(x)=x \cdot \mathrm{e}^{x(1-x)}\), then \(\mathrm{f}(x)\) is
- A increasing in \(\mathbb{R}\)
- B increasing in \(\left(-\frac{1}{2}, 1\right)\)
- C decreasing in \(\mathbb{R}\)
- D decreasing in \(\left[-\frac{1}{2}, 1\right]\)
Answer & Solution
Correct Answer
(B) increasing in \(\left(-\frac{1}{2}, 1\right)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = \frac{\mathrm{d}}{\mathrm{d}x}(x \cdot \mathrm{e}^{x-x^2})\) \(f'(x) = 1 \cdot \mathrm{e}^{x-x^2} + x \cdot \mathrm{e}^{x-x^2} \cdot (1-2x)\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The integrating factor of the differential equation y \(\log _{y}\left(\frac{\mathrm{d} x}{\mathrm{dy}}\right)+x-\log \mathrm{y}=0\)
isMHT CET 2020 Easy - The equation of a line passing through the point \((2,-1,1)\) and parallel to the line joining the points \(\hat{i}+2 \hat{j}+2 \hat{k}\) and \(-\hat{i}+4 \hat{j}+\hat{k}\) isMHT CET 2024 Medium
- The number of integral values of \(p\) in the domain \([-5,5]\), such that the equation \(2 x^2+4 x y-\mathrm{p} y^2+4 x+\mathrm{q} y+1=0\) represents pair of lines, areMHT CET 2023 Medium
- If \(\bar{a}=2 i+3 j-\hat{k}, \bar{b}=-i+2 j-4 \hat{k}\) and \(\bar{c}=i+j+\hat{k}\), then \((\bar{a} \times \bar{b}) \cdot(\bar{a} \times \bar{c})=\)MHT CET 2020 Easy
- The value of \(\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)\) isMHT CET 2022 Easy
- A random variable \(x\) has the following probability distribution. Then value of \(k\) is and \(\mathrm{P}(3 \lt x \leq 6)\) has the value
MHT CET 2024 Easy
More PYQs from MHT CET
- Identify false statement regarding isothermal process from following.MHT CET 2023 Easy
- If the four positive integers are selected randomly from the set of positive integers, then the probability that the number \(1,3,7\) and 9 are in the unit place in the product of 4 -digit, so selected isMHT CET 2012 Medium
- If \(\overline{\mathrm{a}} \cdot\) and \(\overline{\mathrm{c}}\) are unit vectors inclined at \(\frac{\pi}{3}\) with each other and \((\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})) \cdot(\overline{\mathrm{a}} \times \overline{\mathrm{c}})=5\), then the value of \(5[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]=\)MHT CET 2024 Medium
- If \(\log (x+y)=\log (x y)+a\), where a is constant, then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=2\) and \(y=4\) isMHT CET 2022 Medium
- The end product in Hofmann's exhaustive of amines isMHT CET 2022 Medium
- The Boolean expression for 'XOR' gate \(C=(A \oplus B)\) is equal toMHT CET 2024 Easy