Let be continuous on and differentiable on . If and , what does the Mean Value Theorem guarantee?
Answer and explanation
Correct answer: B. for some
- Step 1: State the Mean Value Theorem: there exists at least one number such that .
- Step 2: Substitute and : .
Answer
for some .
Why not the others: '' confuses the average rate with ; '' confuses MVT with Rolle's Theorem or the Intermediate Value Theorem; '' computes without dividing by .
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