The function defined by has critical points (points where ):
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1 markMathematicsLimits, continuity and differentiabilityMean value theorem and Rolle's theoremModerateabout 2 min
DSE 2013 Question 3: Limits, continuity and differentiability
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The function defined by f(x)=x(x-10)(x-20)(x-30) has critical points (points where f′(x)=0): (A) at some x<0 and some x>30. (B) at an x<0, and at some x between 0 and 30. (C) between 0 and 10, 10 and 20, 20 and 30. (D) None of the above captures all the critical points.
Also written as: The function defined by f(x)=x(x-10)(x-20)(x-30) has critical points (points where f'(x)=0):
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.
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