(DG2) Computationally Finding Intervals of Increase / Decrease#
By the end of the lesson you will be able to:
locate the intervals of increase and the intervals of decrease using the first derivative of a function.
Lecture Videos#
Finding Intervals of Increase / Decrease#
Increase / Decrease Test
For the interval \((a,b)\), if \(f\) is differentiable then:
\(f'(x)>0 \iff f\) is increasing
\(f'(x)<0 \iff f\) is decreasing
Critical Number
The number \(x=c\) is a critical number of \(f\) provided either:
and \(c\) is in the domain of \(f\).
Calculate \(f'(x)\)
Find where \(f'(x)=0\) and \(f'(x) \;\text{ DNE}\).
Create a sign chart for \(f'\).
Determine the sign of \(f'\) on each interval.
Example 1#
Find the intervals of increase and the intervals of decrease for function \(f\) with first derivative given below:
Example 2#
Find the intervals of increase and the intervals of decrease for function \(f\) given below:
Example 3#
Find the intervals of increase and the intervals of decrease for function \(f\) given below:
Example 4#
Find the intervals of increase and the intervals of decrease for function \(f\) given below:
Example 5#
Find the intervals of increase and the intervals of decrease for function \(f\) given below: