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Please help me with this problem:
Apply the critical number theorem to find the maximum and minimum values of f(x) = + 1 occur on the interval [-2,1].
What are the maximum and minimum values of f on this interval?
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0. f(x) = .
1. Find f'(x). It is f'(x) = 2x.
2. Write the equation f'(x) = 0. It is 2x = 0.
Solve it. The solution is x = 0.
3. Calculate f(0). It is f(0) = = 1.
4. Calculate f(x) at x = -2. It is f(-2) = = 5.
5. Calculate f(x) at x = 1. It is f(1) = = 2.
6. Compare the values f(-2), f(0) and f(1).
They are 5, 1 and 2.
7. Conclusion: x = -2 gives the maximum, x = 0 gives the minimum in the segment [-2,1].
8. The problem is solved.