For f(x) = -x² + 10x, find the interval on which f is increasing, the interval on which it is…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
For , find the interval on which is increasing, the interval on which it is decreasing, and the turning point.
Need a reminder? The key ideaShow
has its vertex at and opens upward when . Completing the square, , gives the vertex and the range.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The vertex. , a parabola opening downward with its top at .
Step 2. Rising and falling. It increases on and decreases on .
Answer: increasing on , decreasing on , turning at .
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