The function f(x) has a domain of (−∞, −1) ∪ (−1, ∞) and a second derivative given by the following.

Question

f ''(x) = −2(x + 5)^11(x − 6)^7(x + 1)/(x + 1)

Find the x-value(s) of the inflection points of f(x).

 (Enter your answers as a comma-separated list. If there are no inflection points, enter NONE.)

Answer 1

f''(x) = -2(x + 5)¹¹(x - 6)⁷ = 0; x = - 5 or x = 6 x ≠ - 1.

at x = - 5 f''(x) changes sign from - to + and because we have inflection point from concave down to concave up; at x = 6 f''(x) changes sign from + to - and because we have inflection point from concave up to concave down.

Answer 2