Q. 224.5( 2 Votes )

# Determine the int

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

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