Questions from General Calculus


Q: (a) Find the intervals on which f is increasing or

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f(x) = x4 - 2x2 + 3

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Q: (a) Find the intervals on which f is increasing or

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f(x) =sin x + cos x, 0...

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Q: (a) Find the intervals on which f is increasing or

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f(x) =cos2x - 2 sin x,...

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Q: (a) Find the intervals on which f is increasing or

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f(x) = e2x + e-x

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Q: (a) Find the intervals on which f is increasing or

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f(x) = x2 ln x

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Q: Prove the formula for (d/dx)(cos-1x

Prove the formula for (d/dx)(cos-1x) by the same method as for (d/dx)(sin-1x).

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Q: (a) Find the intervals on which f is increasing or

(a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. f(x) = x2 - x - ln x

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Q: Suppose the derivative of a function f is f (x

Suppose the derivative of a function f is f (x) = (x + 1)2 (x – 3)5 (x – 6)4. On what interval is f increasing?

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Q: Use the methods of this section to sketch the curve y =

Use the methods of this section to sketch the curve y = x3 - 3a2x + 2a3, where a is a positive constant. What do the members of this family of curves have in common? How do they differ from each other...

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Q: A graph of a population of yeast cells in a new laboratory

A graph of a population of yeast cells in a new laboratory culture as a function of time is shown. (a) Describe how the rate of population increase varies. (b) When is this rate highest? (c) On what...

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