SOLUTION: Please help me with this problem: Apply the critical number theorem to find the maximum and minimum values of f(x) = {{{x^2}}} + 1 occur on the interval [-2,1]. What are the maxim

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Question 1024912: Please help me with this problem:
Apply the critical number theorem to find the maximum and minimum values of f(x) = x%5E2 + 1 occur on the interval [-2,1]. What are the maximum and minimum values of f on this interval?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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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) = x%5E2 + 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) = x%5E2+%2B+1. 

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) = 0%5E2+%2B+1 = 1.

4.  Calculate  f(x)  at x = -2.  It is  f(-2) = %28-2%29%5E2+%2B+1 = 5.

5.  Calculate  f(x)  at x = 1.   It is  f(1)  = 1%5E2+%2B+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.