Answer:
To find when a function is decreasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing. I will test the values of 0, 2, and 10.
Explanation:
Find the interval(s) where the following function is decreasing. Graph to double check your answer.
y=13x3+2x2−5x−6
Possible Answers:
Always
Never
(−∞,−5)∪(1,∞)
(−5,1)
Correct answer:
(−5,1)
Explanation:
To find when a function is decreasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative.
First, take the derivative:
y′=x2+4x−5
Set equal to 0 and solve:
x2+4x−5=0
(x+5)(x−1)=0
x=−5,1
Now test values on all sides of these to find when the function is negative, and therefore decreasing. I will test the values of -6, 0, and 2.
y′=x2+4x−5
y′(−6)=(−6)2+4(−6)−5=7
y′(0)=(0)2+4(0)−5=−5
y′(2)=(2)2+4(2)−5=7
Since the only value that is negative is when x=0, the interval is only decreasing on the interval that includes 0. Therefore, our answer is:
(−5,1)