Questions from General Calculus


Q: Use the given graph of f to find the following.

Use the given graph of f to find the following. (a) The open intervals on which f is increasing. (b) The open intervals on which f is decreasing. (c) The open intervals on which f is concave upward. (...

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Q: Use the given graph of f to find the following.

Use the given graph of f to find the following. (a) The open intervals on which f is increasing. (b) The open intervals on which f is decreasing. (c) The open intervals on which f is concave upward. (...

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Q: Suppose you are given a formula for a function f.

Suppose you are given a formula for a function f. (a) How do you determine where f is increasing or decreasing? (b) How do you determine where the graph of f is concave upward or concave downward? (c)...

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Q: (a) State the First Derivative Test. (b

(a) State the First Derivative Test. (b) State the Second Derivative Test. Under what circumstances is it inconclusive? What do you do if it fails?

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Q: Sketch the graph of a function that satisfies all of the given

Sketch the graph of a function that satisfies all of the given conditions. (a) f ‘(x) > 0 and f ‘‘(x) < 0 for all x (b) f ‘(x) < 0 and f ‘‘(x) > 0 for all x

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Q: The graph of the derivative f 9 of a function f is

The graph of the derivative f 9 of a function f is shown. (a) On what intervals is f increasing or decreasing? (b) At what values of x does f have a local maximum or minimum?

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Q: Two curves are orthogonal if their tangent lines are perpendicular at each

Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Show that the given families of curves are orthogonal trajectories of each other; that is, every curve...

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Q: The graph of the derivative f 9 of a function f is

The graph of the derivative f 9 of a function f is shown. (a) On what intervals is f increasing or decreasing? (b) At what values of x does f have a local maximum or minimum?

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