Q. 1 A5.0( 1 Vote )

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]

Answer :

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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