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Suppose the derivative of a function f is f '(x) = (x + 1)^2 (x - 3)^5 (x - 6)^4.

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Suppose the derivative of a function f is f '(x) = (x + 1)^2 (x - 3)^5 (x - 6)^4. On what interval is f increasing?
asked Jan 22, 2015 in CALCULUS by anonymous

1 Answer

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Step 1 :

Increasing or decreasing test :

(a) If on an interval, then f  is increasing on that interval.

(b) If on an interval, then f  is decreasing on that interval.

Step 2 :

The function is .

The critical points exist when .

Equate to zero :

The critical points are and .

Consider the test intervals : and .

Interval Test Value Sign of Conclusion
+ +

Decreasing
+ +

Decreasing
+ + +

Increasing
+ + +

Increasing

Thus, The function is increasing on the intervals and .

Combine above two intervals.

Hence, the function is increasing on the interval .

Solution :

The function is increasing on the interval .

answered Jan 22, 2015 by Thomas Apprentice
edited Jan 22, 2015 by Thomas

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