Find the absolute maximum and the absolute minimum values of the following functions in the given intervals:
f(x) = 4x – x2/2 in [–2, 45]
given function is f(x) = 
∴f'(x) = 4 – x
Now,
f'(x) = 0
4 – x = 0
x = 4
Then, we evaluate of f at critical points x = 4 and at the interval [ – 2, 
]
f(4) = 
= 8
f(– 2) = 
f(
) = 
Hence, we can conclude that the absolute maximum value of f on [ – 2, 9/2] is 8 occurring at x = 4 and the absolute minimum value of f on [ – 2, 9/2] is – 10 occurring at x = – 2
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