Which of the following statements is true for all real numbers with ?
Tap an option to check your answer.
1 mark, −0.333333333333333MathematicsLimits, continuity and differentiabilityMean value theorem and Rolle's theoremEasyabout 1 min
DSE 2014 Question 4: Limits, continuity and differentiability
Answer and worked solution
Checking your account…
Plain-text version
Which of the following statements is true for all real numbers a,b with a<b? (A) sin b-sin a≤ b-a (B) sin b-sin a≥ b-a (C) |sin b-sin a|≥ b-a (D) |sin b-sin a|≤|b-a|
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.
Similar questions from other papers
- Derivative of Average cost (AC) = 5 + 2/Q is
- The value of the first derivative of f(x)=(3x³+2x²+x+1)² evaluated at x=2 is (*in integer*).
- What will be the third derivative of the following rational function? y = g(x) = x/(1+x); (x ≠ -1)
- The 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…
- Let f(x) = -3x²(1-x) - 3x(1-x)² - (1-x)³. Then, df(x)/dx =
Question from the DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.