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 › DSE › DSE 2015 › Q37
2 marks, −0.666666666666667Mathematics › Limits, continuity and differentiability › Mean value theorem and Rolle's theoremModerateabout 3 min

DSE 2015 Question 37: Limits, continuity and differentiability

Let a<ba<ba<b be two consecutive, non-repeated roots of a polynomial fff, so f(x)=(x−a)(x−b)g(x)f(x)=(x-a)(x-b)g(x)f(x)=(x−a)(x−b)g(x). Consider: I. g(a)g(a)g(a) and g(b)g(b)g(b) have opposite signs. II. f′(x)=0f'(x)=0f′(x)=0 for some x∈(a,b)x\in(a,b)x∈(a,b). Then

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Let a<b be two consecutive, non-repeated roots of a polynomial f, so f(x)=(x-a)(x-b)g(x). Consider: I. g(a) and g(b) have opposite signs. II. f′(x)=0 for some x∈(a,b). Then (A) both I and II are true (B) only I is true (C) only II is true (D) both I and II are false

Also written as: Let a<b be two consecutive, non-repeated roots of a polynomial f, so f(x)=(x-a)(x-b)g(x). Consider: I. g(a) and g(b) have opposite signs. II. f'(x)=0 for some x in (a,b). Then

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Mean value theorem and Rolle's theorem, part of Limits, continuity and differentiability in Mathematics.

Results linking the average rate of change to a derivative at some point.

TestStop has 13 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Mean value theorem and Rolle's theorem

Similar questions from other papers

  • CUET-PG 2026 · Q24Derivative of Average cost (AC) = 5 + 2/Q is
  • IIT JAM 2026 · Q50The value of the first derivative of f(x)=(3x³+2x²+x+1)² evaluated at x=2 is (*in integer*).
  • UGC-NET 2026 · Q8What will be the third derivative of the following rational function? y = g(x) = x/(1+x); (x ≠ -1)
  • CUET-PG 2025 · Q3The exports of goods of a country, G = G(t) has a growth rate of a/t, and its exports of services, S = S(t) has a growth rate of b/t. What is the growth rate of its…
  • GATE 2025 · Q32Let f(x) = -3x²(1-x) - 3x(1-x)² - (1-x)³. Then, df(x)/dx =

Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.