If f(x)=0x(1t2)cos2tdt, on what interval is f increasing?
The intervalwhere the function is increasing.
i) i) Fundamental Theorem of calculus. If is continuous on and
ii) Increasing test:
If on an interval, then is increasing on that interval.
If on an interval, then is decreasing on that interval.
Differentiating on both sides
By using the fundamental theorem
Now find such that .
These are the critical numbers of , and they divide the domain into three intervals. To determine if is negative or positive for each interval from the signs of the two factors of namely, we shall use the following table.