MediumMathematicsHigh School (11–12)Functions and Calculus › Application of DerivativesNumericalA-LevelAPIBJEE Main
The height of the floor of a long exhibition hall above its lowest corner is modelled by f(x) = x⁴…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The height of the floor of a long exhibition hall above its lowest corner is modelled by metres, where is the distance across the hall in metres, with . Find the critical points. Use the first derivative test to say which gives a local maximum and which gives a local minimum, and find the local extreme values.
Need a reminder? The key ideaShow
A critical point is a value where or does not exist. If changes from to at there is a local maximum, and from to a local minimum. If keeps its sign, there is neither.
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 derivative. .
Step 2. The critical points. at , and . That is critical points.
Step 3. The signs. At , . At , . At , . At , .
Step 4. The kinds. goes to at and at , so these are local minima. It goes to at , a local maximum.
Step 5. The values. and .
Answer: critical points, a local maximum value of and a local minimum value of .
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