Answer:
Option 3 - (-0.7,1)
Step-by-step explanation:
Given : Function [tex]y=2x^3-x^2-4x+5[/tex]
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 [tex]-\infty[/tex] 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 [tex]\infty[/tex] 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.
