# Functions

• May 8th 2013, 11:16 PM
teobai
Functions
I would like some help to solve the following function: Determine the location and nature of the stationary point of the function x3 - 24x2 + 192x + 5
• May 9th 2013, 12:02 AM
ibdutt
Re: Functions
The stationary points of a function are the points where its derivative is zero. In this case
3x^2-48 x + 192 = 0 OR x^2 - 16 x + 64
Find x and corresponding y from the given function.
To know if the stationary point is concave upward or down ward find the second derivative. If it is negative then the at that point the function will be concave downward and if it is positive then it will be concave upward.
• May 9th 2013, 12:40 AM
teobai
Re: Functions
Thank you Ibdutt for your prompt reply. I would like to ask you how did you get this answer: 0 OR x^2 - 16 x + 64
I have tried to understand the logic but I could not follow it. I would be happy if you can break it down for me. Thanks for your time and patience.
• May 9th 2013, 12:52 AM
MarkFL
Re: Functions
We are given:

$f(x)=x^3-24x^2+192x+5$

To find the stationary point(s), we equate the derivative to zero, and so using the power rule term by term, we find:

$f'(x)=3x^2-48x+192=0$

Now, dividing through by 3, we obtain:

$x^2-16x+64=0$

Once you factor, what does this tell you about the sign of the derivative?
• May 9th 2013, 01:36 AM
ibdutt
Re: Functions
Just divide the equation 3x^2 - 48 x + 192 = 0 by 3 and you will get x^2 - 16 x + 64 = 0