Respuesta :
Answer:
C. - 1 and 0 only
Step-by-step explanation:
(x + 1) / x = 0, - 1, 2
inflection points / when sign Changes
+ / - / + / +
"- 1 " "0" 2
^ ^
"Hope this helps"
The graph of f has inflection points when x = 0 and -1.
Given that,
If graph = f"(x) = x(x + 1)(x - 2)^2
We have to determine,
The graph of f has inflection point when x is.
According to the question,
Inflection point is the point in which the rate of slope changes in increasing to decreasing order or vice versa.
These points are generally not local maxima or minima but stationary points.
[tex]f''(x) = 0[/tex]
Therefore,
The graph of f has inflection point at,
[tex]f''(x) = x (x+1) (x-2)^{2} = 0\\\\x = 0 \ and \ x+1 = 0 \ \ = x = -1\\\\ or \ x-2 = 0 , \\\ \ \ = x =2[/tex]
On taking intersection of these points,
The graph has inflection points at x = 0 and -1.
Hence, The graph of f has inflection points when x = 0 and -1.
To know more about Inflection points click the link given below.
https://brainly.com/question/2289668
