# Thread: maximum and minimum of functions

1. ## maximum and minimum of functions

Is there a mistake?

$\displaystyle y=x^3-6x^2+9x$

$\displaystyle y'=3x^2-12x+9$

$\displaystyle y'=0$

$\displaystyle x=3 and x=1$

Extreme local:
P(1,4) ---> Point maximum

P(3,0) --->
Point minimum

$\displaystyle y''=6x-12$

Point of inflection:
P(2,2)

Sorry. Is there any way to put graphic here?

2. Originally Posted by Apprentice123
Is there a mistake?

$\displaystyle y=x^3-6x^2+9x$

$\displaystyle y'=3x^2-12x+9$

$\displaystyle y'=0$

$\displaystyle x=3 and x=1$

Extreme local:
P(1,4) ---> Point maximum

P(3,0) --->
Point minimum

$\displaystyle y''=6x-12$

Point of inflection:
P(2,2)

Sorry. Is there any way to put graphic here?
Yes, it's all correct.

(To put graphic, click on 'Manage Attachments' (browse and attach picture) when you click advanced reply)

3. Originally Posted by Apprentice123
Is there a mistake?

$\displaystyle y=x^3-6x^2+9x$

$\displaystyle y'=3x^2-12x+9$ Good

$\displaystyle y'=0$ Good

$\displaystyle x=3 and x=1$ Good

Extreme local:
P(1,4) ---> Point maximum Good

P(3,0) --->
Point minimum Good

$\displaystyle y''=6x-12$ Good

Point of inflection:
P(2,2) Good

Sorry. Is there any way to put graphic here?

The graph of $\displaystyle y=x^3-6x^2+9x$ makes this all seem reasonable:

--Chris

4. thank you