Question

Where is the function decreasing? Urgent running out of time on the test.

a) At critical points
b) In the interval where the derivative is negative
c) At the x-intercepts
d) In the interval where the derivative is positive

Answer 1

A function is decreasing in the intervals where its derivative is negative, which corresponds to the slopes being negative and the function going downhill. The correct answer is option B.

Step-by-step explanation:

The question pertains to where a function is decreasing. The answer to where a function is decreasing is b) In the interval where the derivative is negative.

A function is said to be decreasing on an interval if the function values decrease as the input values increase within that interval. The derivative of a function gives us the rate of change or the slope of the function at any given point. When the derivative is negative, the slope of the function is negative, which means the function is going downhill or decreasing. It is not necessarily decreasing at critical points, x-intercepts, or where the derivative is positive, as those could correspond to points or intervals where the function is increasing, constant, or changing concavity.

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.