Question

The function f(x) = x³+6x²+9x+3 is decreasing for

A. 1 < x < 3

B. x > 1

C. x < 1

D. x < 1 or x > 3

Answer 1

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