Answer :

Given: f(x) = x4 - 8x3 + 22x2 - 24x + 21


Finding f (x)


f (x) = 4x3 - 24x2 + 44x - 24


formula:


f (x) = 4(x3 - 6x2 + 11x - 6)


f (x) = 4(x - 1) (x - 2) (x - 3)


for finding the maxima or minima f (x) = 0 at that point


f (x) = 0 at x = 1, x = 2 and x = 3


the intervals are ( - ∞, 1) (1, 2) (2, 3) (3, ∞)


since f (x) > 0 in (1, 2) and (3, ∞)


therefore f(x) is strictly increasing in (1, 2) and (3, ∞) and strictly decreasing in ( - ∞, 1) and (2, 3).


OR


Given: f(x) = sec x + log cos2x


Finding f (x)


f (x) = sec x tan x - 2tan x


Formula:


f (x) = tan x (sec x - 2)


for finding the maxima or minima f (x) = 0 at that point


f (x) = 0 at tan x = 0 or sec x = 2


therefore, solution is x = π or


now finding f” (x) to check whether the point is maxima or minima


f” (x) = sec x tan2x + (sec x - 2) sec2x


Formula:


substituting the points


which is positive hence it is minimum


which is negative hence it is maximum


which is positive hence it is minimum


Therefore, we can conclude that


Maximum value


Minimum value


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