Question

Given the function h(x)=-2√x, which statement is true about h(x)?

O The function is decreasing on the interval (0,0).
O The function is decreasing on the interval (-∞, 0).
O The function is increasing on the interval (0, ∞).
O The function is increasing on the interval (-∞, 0).

Answer 1

The statement "The function is decreasing on the interval (0, ∞)" is true about h(x).

To see why, let's take the derivative of h(x) and examine its sign:

h(x) = -2√x

h'(x) = -2/(2√x) = -1/√x

Since √x is always positive, h'(x) is negative for all x > 0. This means that h(x) is decreasing on the interval (0, ∞).

Therefore, the correct answer is: The function is decreasing on the interval (0, ∞).