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Calculus Questions on Limits, Derivatives, and Extremum Points

Explore calculus questions related to limits, derivatives, and extremum points. Test your knowledge with these critical thinking questions and enhance your understanding of calculus concepts.

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Calculus Questions on Limits, Derivatives, and Extremum Points

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  1. Class 26: Question 3 The limit A. Does not exist because∞ - ∞ is not defined.B. Converges to 1. C. Converges to 0.D. Is ∞ because xe1/x grows faster than x.

  2. Class 28: Question 1 The duration of daylight L in minutes (sunrise to sunset) x kilometers north of the equator on May 17 is given by the function L=f(x). What are the units of measurement of the second derivative f''(4000)? A. kilometers/minute B. minutes/kilometer.C. kilometer/minute2. D. minutes/kilometer2.E. minutes2/kilometer2.

  3. Class 28: Question 2 The derivative of a function is negative everywhere on the interval x=2 to x=3.Where on this interval does f(x)have its maximum value? A. At x=2.B. At x=3.C. Somewhere between x=2 and x=3.D. It does not have a maximum since the derivative is never zero.E. We can not tell if it has a maximum since we don’t know where the second derivative is negative.

  4. Class 28: Question 3 TRUE or FALSE: If f′′(a)=0, then f has an inflection point at a A. TRUE B. FALSE.

  5. Class 28: Question 4 TRUE or FALSE: A local maximum of f only occurs at a point where f′(x)=0. A. TRUE B. FALSE.

  6. Class 28: Question 5 TRUE or FALSE: If x=p is NOT a local extremum of f, then x=p is not a critical point of f. A. TRUE B. FALSE.

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