Using Absolute Maximum and Minimum,
the absolute Maximum value of f(x) is 8.5 at x = 8 and absolute minimum value of f (x) is 2.44 at x = 0.2 on given interval [0. 2, 8].
we have given function is
f(x) = x + 4/x ---(1)
and interval [ 0.2 , 8]
firstly, find first order derivative of f(x)
f'(x) = 1 - 4/x²
now, f'(x) = 0 then 1 - 4/x^2 =0
=> 4/x²= 1
=> x² = 4
=> x = 2 or -2
that is 2 and -2 are critical points but only critical number 3 belong to given closed interval.
we evaluate the value of "f" at critical point, x =3 and at ends points of given interval [0.2, 8].
f(3) = 3 + 4/3 = 4.33 , f(0.2) = 0.2 + 4/0.2 = 2.44
, f(8) = 8 + 4/8 = 17/2 = 8.5
Hence, the absolute Maximum value of f on [0.2,8] is 8.5 occuring at x = 8 and absolute minimum value of f on [0.2,8] is 2.44 occuring at x= 0.2 ..
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