Graph the function y = 2x3 – x2 – 4x + 5. to the nearest tenth, over which interval is the function decreasing?
(1, ∞)
(–∞, –0.7)
(–0.7, 1)
(–1, 0.7)

On (-2/3, 1) the given function is decreasing

Step-by-step explanation:

Do you know calculus?  If so:

Differentiate y = 2x^3 – x^2 – 4x + 5 and set the derivative = to 0:

dy/dx = 6x^2 - 2x - 4 = 0, or 3x^2 - x - 2 = 0.

This factors as follows:  (x - 1)(3x + 2) = 0.

The roots of this equation are {1, -2/3}.  

Plot these two roots on a number line and then set up intervals as follows:

(-infinity, -2/3), (-2/3, 1), (1, infinity)

Choose a test number from each interval:  { -1, 0, 2 }

By evaluating the derivative 6x^2 - 2x - 4 at each of these three test numbers, we get:

dy/dx = 6x^2 - 2x - 4 is positive on (-infinity, -2/3), and so we conclude that the given function is increasing on that interval.

dy/dx = 6x^2 - 2x - 4 is negative on (-2/3, 1), and so we conclude that the given function is decreasing on that interval.   To the nearest tenth:

(-0.7, 1)