Question

f (x ) = x^(3) - 4x . Which describes an interval, rounded to the nearest tenth, in which the function is decreasing?

Answer 1

To find where the function f(x) = x^3 - 4x is decreasing, we can find the derivative and identify the intervals where it is negative.

Step-by-step explanation:

To determine where the function f(x) = x^3 - 4x is decreasing, we can find the derivative of the function and identify the intervals where the derivative is negative.

First, we differentiate the function using the power rule, which states that the derivative of x^n is n*x^(n-1). In this case, the derivative of f(x) is f'(x) = 3x^2 - 4.

Next, we set f'(x) < 0 and solve for x to find the intervals where the function is decreasing.

3x^2 - 4 < 0 --> 3x^2 < 4 --> x^2 < 4/3 --> -sqrt(4/3) < x < sqrt(4/3).