Find the absolute maximum and the absolute minimum values of the following functions in the given intervals:
f(x) = 3x4 – 8x3 + 12x2 – 48x + 25 in [0, 3]
given function is f(x) = 
Now,
f'(x) = 0
x = 2 or x2 + 2 = 0 for which there are no real roots.
Therefore, we consider only x = 2 
[0, 3].
Then, we evaluate of f at critical points x = 2 and at the interval [0, 3]
f(2) = 
f(2) = 48 – 64 + 48 – 96 + 25 = – 39
f(0) = 
f(3) = 
Hence, we can conclude that the absolute maximum value of f on [0, 3] is 25 occurring at x = 0 and the minimum value of f on [0, 3] is – 39 occurring at x = 2
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