# Veriyfing that point given is either maximum or minimum

• February 25th 2011, 09:16 PM
Devi09
Veriyfing that point given is either maximum or minimum
Use an algebraic strategy to verify that the point given for the function is either a maximum or minimum.

f(x) = x3 - 3x; (-1,2)

The answer should be 0 yet i get another answer. This is what i did:[COLOR=rgb(0, 0, 0)]

[/COLOR] $(a+h)-(a)/h=(-1+h)-(-1)/h=(-1+h)^3-(-3(-1))/h$

$(-1+h)(-1+h)(-1+h)=(1-h-h+h^2)(-1+h)=-1+3h-3h^2+h^3$

$(-1+3h-3h^2+h^3-3/h$

"h's" cancel

$-1+3-3h+h^2-3=h^2-3h-1$

$h=0.01,h=-0.01$

$(0.01)^2-3(0.01)-1=-1.0299$

$(-0.01)^2-3(-0.01)-1=-0.9699$

$-1.0299+(-0.9699)/2=-0.9999$

It should = 0 however and the slopes should be negative right side and positive left side I believe proving it is a maximum.
• February 25th 2011, 09:45 PM
sa-ri-ga-ma
Check the first step.
It should be

$\frac{( a + h) - a}{h}$ It becomes

$\frac{[(-1 + h)^3 - 3(-1 +h)] - [ (-1)^3 -3(-1)]}{h}$

Now proceed.
• February 25th 2011, 09:58 PM
Devi09
Yeh that's what I did. I'm new with latex so I really ment h dividing that whole part not just "a" which gives me the answer that I got
• February 25th 2011, 10:39 PM
sa-ri-ga-ma
Simplify the numerator and see what you get.
• February 26th 2011, 10:11 AM
Devi09
Alright so I tried again hopefully correctly but in the end I still didn't get that 0 i'm looking for

[tex](-1+h)^3-3(-1+h)-[(-1)^3-3(-1)]/h[\MATH]

[tex]-1+3h-3h+3h^3-[-1+3][\MATH]

[tex]-1+1-3+3h-3h+3h^3/h[\MATH]

"h's cancel plus other numbers"

[tex]3h-3[\MATH]

[tex]3(0.01)-3 = -2.97[\MATH]

[tex]3(-0.01)-3 = -3.03[\MATH]

[tex]-2.97+(-3.03)/2 = -3[\MATH]

This time i get -3 instead of 0 and both "h's" left and right sides are negative instead of being left positive and right negative proving it to be a maximum
• February 26th 2011, 02:12 PM
Devi09
Alright after many many tries i managed to get a tangent of 0.0001. Not 0 but really really close so I guess that's good enough and I also got the right side to be negative and left side positive proving its a maximum. The problem was that I made a simple but at the same time major mistake simplifying.