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UaRemomGAY
05.03.2020 •
Mathematics
Consider the following. (If an answer does not exist, enter DNE.) f '(x) = x2 + x − 20 (a) Find the open intervals on which f '(x) is increasing or decreasing.
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Ответ:
f'(x) is increasing in the open interval (-1/2, +∞), and it is decreasing in the interval (-∞, -1/2).
Step-by-step explanation:
f'(x) is a quadratic function with positive main coefficient, then it will be decreasing until the x-coordinate of its vertex and it will be increasing from there onwards. The x-coordinate of the vertex is given by the equation -b/2a = -1/2. Hence
- f'(x) is incresing in the interval (-1/2, +∞)
- f'(x) is decreasing in the interval (-∞, -1/2)
Ответ: