Question

The derivative of the function f is given by f′(x)=x^2−2−3xcosx. On which of the following intervals in [−4,3] is f decreasing?

Answer 1

To determine where the function f is decreasing, we need to find where the derivative of f is negative. Given that the derivative of f is f′(x)=x^2−2−3xcosx, we set the derivative equal to zero and solve for x to find the critical points.

Step-by-step explanation:

To determine where the function f is decreasing, we need to find where the derivative of f is negative. Given that the derivative of f is f′(x)=x^2−2−3xcosx, we set the derivative equal to zero and solve for x to find the critical points:

x^2 - 2 - 3xcosx = 0

Unfortunately, this equation cannot be solved analytically. We can use numerical methods or graphing technology to approximate the critical points. Then, we can test the intervals between the critical points and endpoints to determine where f is decreasing.