Practice question · Put in order
Order the steps of finding the extreme values of a function on a closed interval.
- Solve f'(x) = 0 to locate the critical points
- Differentiate the function
- Compare the values and pick the largest and the smallest
- Add the two endpoints of the interval to the list of candidates
- Evaluate the function at every candidate point
Hints
- The derivative must exist before it can be set to zero.
- Comparison is the last act, and it needs the complete candidate list.
Show the answer
- Differentiate the function
- Solve f'(x) = 0 to locate the critical points
- Add the two endpoints of the interval to the list of candidates
- Evaluate the function at every candidate point
- Compare the values and pick the largest and the smallest
Why
Differentiate, solve, add the endpoints, evaluate, compare. Comparing before the endpoints are on the list is exactly the error that hides an extreme value sitting at a boundary.
Practise Applications of Derivatives
The app has 5 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
More questions on Applications of Derivatives
- Select every statement that is TRUE of the second derivative.
- Complete the definition of an inflection point.
- Each item reports how the sign of f' behaves as x passes through a critical point. Sort them.
- A point where f'(x) = 0 is always a maximum or a minimum.
- A physics engine integrating with a smaller timestep is more accurate and eventually gets worse below a…