find the maximum or the minimum

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calcnovis

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Joined
Mar 22, 2013
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I was asked to find the maximum or the minimum of x3+3x2+3x

My friend told me to do it this way:

f(x)=x3-3x2
f(x)=0
x3-3x2=0
x(x2-3x)=0
x=0x2-3x=0
x(x-3)=0
x=0
x=3
answer= 0,3

But my professor gave me this formula to use
d2y/dx2

Am I doing this wrong?
 
calcnovis said:
I was asked to find the maximum or the minimum of x3+3x2+3x

My friend told me to do it this way:

f(x)=x3-3x2
f(x)=0
x3-3x2=0
x(x2-3x)=0
x=0x2-3x=0
x(x-3)=0
x=0
x=3
answer= 0,3

But my professor gave me this formula to use
d2y/dx2

Am I doing this wrong?
Click to expand...

By that method, you are finding roots of the function (instead of maxima or minima)

For that you need to first

(1) calculate f'(x) = \(\displaystyle \dfrac{dy}{dx}\)

(2) Then find roots of f'(x)

(3) Then calculate f"(x) = \(\displaystyle \dfrac{d^2y}{dx^2}\)

(4) Now evaluate f"(x) at the roots found in step (2)

(5) If f"(x) < 0 you have a maxima, and if f"(x) > 0 it is a minima
 
Sorry, but I'm lost.

Could you expand on that? You don't need to give me the answer, but I could use the help.

Thank you.
 
calcnovis said:
Sorry, but I'm lost.

Could you expand on that? You don't need to give me the answer, but I could use the help.

Thank you.
Click to expand...

Exactly where are you lost?

Do you know how to find \(\displaystyle \dfrac{dy}{dx}\) of the function in question (y = x3+3x2+3x)?
 
Sorry, I am new to calculus and I don't know how to find [FONT=MathJax_Math]d[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Math]d[/FONT][FONT=MathJax_Math]x[/FONT] of the function in question (y = x3+3x2+3x)
 
calcnovis said:
Sorry, I am new to calculus and I don't know how to find \(\displaystyle \dfrac{dy}{dx}\)of the function in question (y = x3+3x2+3x)
Click to expand...

The only other method could be to use graphical method - where you plot the function and visually (graphically) locate the maxima/minima.
 
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