stationary points?

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July 19th 2010, 02:23 PM
arslan

stationary points?

1. For the following function:

y= x^3/3+ 2x^2 + 3x - 1

a. Find the stationary points.
b. Use the second-order derivatives to test whether the stationary points are at a
maximum or minimum value of.

thank you for your help
July 19th 2010, 02:46 PM
Also sprach Zarathustra

a. find f''(x), then x1 and x2 of f'(x)=0
b. find f''(x), if f''(xt)>0 then xt min. if f''(xt),0 xt max. if f''(xt)=0 and f'''(xt)!=0 then it is nor max/min.
July 20th 2010, 05:08 AM
arslan

thanks however i am clueless to finding f''(x), then x1 and x2 of f'(x)=0
July 20th 2010, 07:10 AM
yeKciM

$f'_(x)=x^2+4x+3$

when u put $f'(x)=0$ means that $x^2+4x+3=0$

$x_1=-1 , x_2=-3$ There u have stationary points...

$f''(x)=(f'(x))'=2x+4$

lol... u can go from here ?

just put stationary points in $f''_{(x)}$

$f''_{(x_1)}=2$ so it's min because it's $f''_{(x_1)}>0$
$f''_{(x_2)}=-2}$ so it's max because it's $f''_{(x_2)}<0$

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