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Find the absolute maximum and the absolute minimum values of the following functions in the given intervals : f(x) = (x – 1)2 + 3 in [–3, 1] |
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Answer» Given function is : f(x) = (x – 1)2 + 3 ∴f'(x) = 2(x – 1) Now, f'(x) = 0 2(x – 1) = 0 x = 1 Then, We evaluate of f at critical points x = 1 and at the interval [– 3, 1] f(1) = (1 – 1)2 + 3 = 3 f(– 3) = (– 3 – 1)2 + 3 = 19 Hence, We can conclude that the absolute maximum value of f on [ – 3, 1] is 19 occurring at x = – 3 and the minimum value of f on [ – 3, 1] is 3 occurring at x = 1 |
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