Question

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)

Answer 1

Option 3 - (-0.7,1)

Explanation:

Given : Function
`y=2x^3-x^2-4x+5`

To find : Over which interval is the function decreasing?

Solution :

First we plot the graph using graphing calculator.

Refer the attached figure below.

Now, Examining the graph

From
`-\infty` to (-0.667,6.63) the graph is increasing as the curve is increasing.

From (-0.667,6.63) to (1,2) the graph decreasing as the curve is decreasing.

From (1,2) to
`\infty` the graph is increasing as the curve is increasing.

So, The interval in which the function is decreasing is given by (-0.667,1)

Round to nearest tenth, (-0.7,1)

Therefore, Option 3 is correct.