APPLICATIO OF FIRST DERIVATIVES PRACTICE QUESTIONS

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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