Question

The function f(x) has a domain of (−[infinity];[infinity]) and a second derivative given by the following. f

′′
(x)=−4(x+4⁾⁵(x−5)Find the x-value(s) of the inflection points of f(x).

Answer 1

The x-values of the inflection points of the function f(x) are x = -4 and x = 5.

Step-by-step explanation:

To find the x-values of the inflection points of the function f(x), we need to identify the values of x for which the second derivative changes sign. In this case, the second derivative is given by f''(x) = -4(x+4)(x-5).

To determine the x-values of the inflection points, we set f''(x) equal to zero and solve for x.

-4(x+4)(x-5) = 0
x+4 = 0 or x-5 = 0
x = -4 or x = 5

Therefore, the x-values of the inflection points of f(x) are x = -4 and x = 5.