Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › JNU › JNU SSS 2018 › Q24
1 mark, −0.25Mathematics › Single-variable optimisation › Optimisation on a closed intervalModerateabout 1 min

JNU SSS 2018 Question 24: Single-variable optimisation

Let y=f(x)y = f(x)y=f(x), where x∈[a,b]x \in [a, b]x∈[a,b] and b>ab > ab>a, be a continuously differentiable function. Suppose f(x)f(x)f(x) attains maximum at x=x∗x = x^*x=x∗. Then it is always true that

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Let y = f(x), where x ∈ [a, b] and b > a, be a continuously differentiable function. Suppose f(x) attains maximum at x = x*. Then it is always true that (A) f′(x*) = 0 (B) f′′(x*) < 0 (C) f′(x*) = 0 and f′′(x*) < 0 (D) Cannot say

Also written as: Let y = f(x), where x in [a, b] and b > a, be a continuously differentiable function. Suppose f(x) attains maximum at x = x*. Then it is always true that

Single-variable optimisation has come up 37 times in 6 exams since 2010.

What this question tests

This question is on Optimisation on a closed interval, part of Single-variable optimisation in Mathematics.

Global maxima and minima when the domain is bounded, including endpoints and existence.

TestStop has 13 past-paper questions on this subtopic.

Practise Single-variable optimisationMore on Optimisation on a closed interval

Similar questions from other papers

  • UGC-NET 2025 · Q78A company has determined that total cost C, total revenue R and the number of units produced X are related as C = 100 + 0.015 X^2 and R = 3X. Find the product level X…
  • IIT JAM 2023 · Q59For k∈ℝ, let f(x)=x⁴+2x³+kx²-k. If x=3/2 is a local minimum of f and m is the global minimum value, then f(0)-m is (in integer).
  • UGC-NET 2023 · Q24Suppose f(.) is a continuous function over a closed and bounded interval [a, b]. Then there exists a point d in [a, b] where f(.) has a minimum, and a point c in [a, b]…
  • JNU SIS 2021 · Q20Let f(x) = x², and the domain of x is [1, 2]. Which of the following statements is true?
  • UoH 2021 · Q76If the demand function for the product of a firm is p = √(1350 - 6q), find the output level that maximizes total revenue.

Question from the JNU SSS 2018 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.