Q. 6 C3.6( 24 Votes )

# Find the interval

Answer :

It is given that function f(x) = –2x3 – 9x2 – 12x + 1

f’(x) = -6x2 – 18x + 12

f’(x) = -6(x2 +3x + 6)

f’(x) = -6(x + 1)(x + 2)

If f’(x) = 0, then we get,

x = -1 and -2

So, the points x = -1 and x = -2 divides the real line into two disjoint intervals,

(-∞,-2), (-2,-1) and (-1,∞)

So, in interval (-∞,-2),(-1,∞)

f’(x) = -6(x + 1) (x +2) < 0

Therefore, the given function (f) is strictly decreasing for x < -2 and x>-1.

So, in interval (-2.-1)

f’(x) = -6(x + 1)(x+2) > 0

Therefore, the given function (f) is strictly increasing for -2 < x < -1.

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