Find the absolute extrema of the following functions on the given closed interval.
(i) f (x) = x3 − 12x + 10 ; [1, 2] Solution
(ii) f(x) = 3x4-4x3 ; [-1, 2] Solution
(iii) f(x) = 6x4/3 - 3x1/3 ; [-1, 1] Solution
(iv) f(x) = 2 cos x + sin 2x ; [0, π/2] Solution
Find the intervals of monotonicities and hence find the local extremum for the following functions:
(i) f(x) = 2x3 + 3x2 −12x Solution
(ii) f(x) = x/(x-5) Solution
(iii) f(x) = ex/(1-ex) Solution
(iv) f(x) = (x3/3) - log x Solution
(v) f(x) = sinx cosx + 5, x ∈ (0, 2π) Solution
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