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Justifying Theorem Conditions
Grade Level
Calculus I
CAL1.94 Justifying Theorem Conditions
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Let q(x)=|x³| on [−1,1]. Which option correctly guarantees there exists c in (−1,1) with q′(c)= (q(1)−q(−1)) ÷ (1−(−1))?
A
Extreme Value Theorem is needed because q has an absolute maximum.
B
Rolle’s Theorem applies since q(−1)=q(1) and q′(0) does not exist.
C
Mean Value Theorem does NOT apply because absolute value prevents differentiability at x=0.
D
Mean Value Theorem; q is continuous on [−1,1] and differentiable on (−1,1), including at x=0.
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