Question

Suppose f '(x) = xe^−x^2

Answer 1

Answers:

• (a) The function is increasing on the interval (0, infinity)
• (b) The function is decreasing on the interval (-infinity, 0)

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Explanation:

You should find that the derivative is entirely negative whenever x < 0. This suggests that the function f(x) is decreasing on this interval. So that takes care of part (b).

The interval x < 0 is the same as -infinity < x < 0 which then translates to the interval notation (-infinity, 0)

Similarly, you should find that the derivative is positive when x > 0. So the function is increasing on the interval (0, infinity)