- Topic
- Optimization
- Difficulty
- Standard
- Suggested time
- 4 min
- Marks
- 2
Optimization practice question 18
A student finds the maximum value of the function below on as shown. Find the first line that is wrong.
On a closed interval, where else can the maximum sit besides a critical point?
Evaluate at and at as well.
Theory UBC Math 100 §8CLP-1 §3.5Key results
Corrected working
Strategy
The candidates are the critical points inside the interval and both endpoints; evaluate f at each and compare.
Working
Critical points, both inside [−2, 3].
Evaluate at the four candidates.
The endpoint wins.
Answer
The answer is the maximum value is 18, at x = 3.
Check
Already at x = 2 the value f(2) = 2 matches the local maximum, and f keeps rising after that, to f(3) = 18.
Where this goes wrong
Comparing only the critical points. On a closed interval the endpoints are candidates, and here one of them is the maximum.
Leans on
Finding critical points, from Differentiation rules
Try a similar question
Find the global minimum value of on the closed interval .Saved in this browser only.