GATE CE 2019 Set 1 — Question 36
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumLocal Maxima & MinimaCalculusEngineering Mathematics
Engineering Mathematics → Calculus → Local Maxima & Minima
Last updated
Question
Which one of the following is NOT a correct statement?
Correct answer
(B) The function (x)^(1/x), (x 0), has the global minima at x = e
Solution
Let for . To find the extrema, we take the derivative:
Differentiating both sides with respect to :
Setting gives .
For , (function is increasing).
For , (function is decreasing).
Therefore, is a point of global maximum. Statement (A) is correct, and statement (B) is incorrect.
For (C), is a monotonic increasing function from to , so it has no global extrema. Correct.
For (D), for all and , so it has a global minimum at . Correct.
Differentiating both sides with respect to :
Setting gives .
For , (function is increasing).
For , (function is decreasing).
Therefore, is a point of global maximum. Statement (A) is correct, and statement (B) is incorrect.
For (C), is a monotonic increasing function from to , so it has no global extrema. Correct.
For (D), for all and , so it has a global minimum at . Correct.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.