Is f(x)=(x−3)(x+11)(x−7) 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+8x−33 and
(x2+8x−33)(x−7)
=x3−7x2+8x2−56x−33x+231
=x3+x2−89x+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+x2−89x+231 so f'(x)
=3x2+2x−89 and f'(-1)
=3(−1)2+2(−1)−89=3−2−89=−88<0 hence f(x) is decreasing at x = - 1