Question

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?

Answer 1

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 .