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]
given function is f(x) = 
∴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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