Is f(x)=(x3)(x+11)(x7) increasing or decreasing at x=1?

1 Answer
Feb 14, 2016

f(x) is decreasing at x = -1

Explanation:

distribute the brackets before differentiating , is probably ' better' than using the 'product rule', in this case.

(x - 3 )(x + 11 ) = x2+8x33

and (x2+8x33)(x7)

=x37x2+8x256x33x+231
=x3+x289x+231

to test whether the function is increasing/decreasing, require to check the value of f'(-1)

• If f'(-1) > 0 then f(x) is increasing at x = -1

• If f'(-1) < 0 then f(x) is decreasing at x = -1

hence f(x) = x3+x289x+231

so f'(x) =3x2+2x89

and f'(-1)=3(1)2+2(1)89=3289=88<0

hence f(x) is decreasing at x = - 1