MediumMathematicsHigh School (11–12)Functions and Calculus › Application of DerivativesNumericalA-LevelAPIBJEE Main
A company's weekly profit, in thousands of dollars, is modelled by f(x) = 2x³ - 15x² + 36x + 1…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A company's weekly profit, in thousands of dollars, is modelled by , where is the number of hundreds of units made. Use the second derivative test to find the values of with a local maximum and a local minimum of the profit, and the local extreme values themselves.
Need a reminder? The key ideaShow
If , then gives a local maximum and a local minimum. If , use the first derivative test. On a closed interval , compare at the end points and at the critical points inside.
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 critical points. , so and .
Step 2. The second derivative. .
Step 3. At . , so there is a local maximum, with .
Step 4. At . , so there is a local minimum, with .
Check. The local maximum is larger than the local minimum even though it comes first. The two values are close because the graph only wiggles a little.
Answer: a local maximum of , a local minimum of , and .
Discussion (0)
Log in to join the discussion.
Loading…