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 }
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.
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.
We are given:
$\displaystyle f(x)=x^3-24x^2+192x+5$
To find the stationary point(s), we equate the derivative to zero, and so using the power rule term by term, we find:
$\displaystyle f'(x)=3x^2-48x+192=0$
Now, dividing through by 3, we obtain:
$\displaystyle x^2-16x+64=0$
Once you factor, what does this tell you about the sign of the derivative?