Calculus: 1,001 Practice Problems For Dummies (+ Free Online Practice) by Jones Patrick

Author:Jones, Patrick
Language: eng
Format: epub
ISBN: 9781118496732
Publisher: Wiley
Published: 2014-07-02T13:17:02+00:00

Therefore, f (x) is concave up on the intervals (–∞, –2), , and (2, ∞), and f (x) is concave down on the intervals and .

470. concave up on , ; concave down on the intervals (0, 0.253), ,

Begin by finding the first and second derivatives of the function f (x) = 2 cos x – sin(2x):

Next, set each factor of the second derivative equal to zero and solve: cos x = 0 has the solutions and , and 4 sin x – 1 = 0, or , has the solutions and x = π – 0.253.

To determine the concavity on the intervals (0, 0.25), , , , and , pick a point from each interval and substitute it into the second derivative to see whether it's positive or negative. Using the values x = 0.1, , , x = π, and gives you the following:

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