# Calculus about inflection point, maxima and minima

How many inflection points does the graph of g(x) have? What is the global maxima and minima ?

My answer was : There are 0 inflection point because they did not pass the Y axes so it did not have a change in sign. Maxima at x= 0 and Minima at x= 3, -3 ?

Is that right or totally wrong ?

• are you asking about the inflection points and maxima and minima for function $g(x)$ or $g^{\prime}(x)$? – JEET TRIVEDI Jun 26 '14 at 23:45
• @JEETTRIVEDI g(x) – John Jun 26 '14 at 23:48

Inflection points are points where $g^{\prime \prime}(x)=0$, so in your case, you have 3 inflection points, $x=0,x=3,x=-3$

Maxima are points where $g^{\prime}(x)=0$ and $g^{\prime \prime}(x)<0$ and Minima points are points where $g^{\prime}(x)=0$ and $g^{\prime \prime}(x)>0$

• wrong answer !! – John Jun 27 '14 at 0:39
• feel free to correct it...or point out the error. Constructive criticism is always appreciated. – JEET TRIVEDI Jun 27 '14 at 0:40
• It was regarding the inflection point it wasn't 3 points. I tried Two and none also but they were false too ;/ – John Jun 27 '14 at 0:46
• ok, admittedly it's hard to tell whether the graph has slope 0 at $x=\pm 3$, it may be that it doesn't. In that case, the only one that I can see for sure as an inflection point is $x=0$ – JEET TRIVEDI Jun 27 '14 at 0:49
• What about the minima and maxima what will it be ? – John Jun 27 '14 at 1:06