The function f(x) = x3+6x2+9x+3 is decreasing forA. 1 < x < 3B. x > 1

The function f(x) = x3+6x2+9x+3 is decreasing forA. 1 1C. x 3

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The function f(x) = x3+6x2+9x+3 is decreasing forA. 1 1C. x 3

1.	The function f(x) = x3+6x2+9x+3 is decreasing forA. 1 < x < 3B. x > 1C. x < 1D. x < 1 or x > 3
Answer» Given: f(x) = x³+6x²+9x+3. f’(x) = 3x²+12x+9 = 0 f’(x) = 3(x²+4x+3) =0 f’(x) = 3(x+1)(x+3) = 0 x = -1 or x = -3 for x > -1 f(x) is increasing for x < -3 f(x) is increasing But for -1 < x < -3 it is decreasing

Answer»

Given:

f(x) = x³+6x²+9x+3.

f’(x) = 3x²+12x+9 = 0

f’(x) = 3(x²+4x+3) =0

f’(x) = 3(x+1)(x+3) = 0

x = -1 or x = -3

for x > -1 f(x) is increasing

for x < -3 f(x) is increasing

But for -1 < x < -3 it is decreasing