|10-07-2009, 06:14 PM||#1|
Join Date: Sep 2005
Location: Los Angeles, CA
Those fluent in Calculus
I've taken the courses already but I'm in a class that I need to apply some of the knowledge... quick question...
For a parabola, say y = 100x - 2x^2 , how do I find the highest point of the parabola (max of Y)? Systematically that is. I know for this example you can graph it and find the midpoint and calculate your answer, but is there another way to do it that involves finding the derivative?
In this example, 0 and 50 are the X-intercepts, and it is a perfect looping parabola therefore 25 would be the mid point and the point where Y is max.
Is there another way to prove this? Thanks!
|10-20-2009, 02:12 PM||#2|
Join Date: Nov 2005
at the highest point, the slope = 0 and it's also an inflection point.
y'(x) = slope @ x
y'(x) = 100-4x
y'(x) = 0 = 100-4x, so x = 25.