max/min (1 Viewer)

[crammy90]

so i know we get x' = 0, solve for x, sub this x in x'' and then if >0 is min n what not.
i remember a question that said "give reasoning" as to why you are doing stuff
- why do we get x' = 0 and do the succeeding steps?
what does x' give us and what not
like i know x' is gradient for a curve, but what is it for a box lol :S

 

[Aplus]

dy/dx = 0 if the point is a stationary point, hence horizontal line. Vertical line is undefined or infinite gradient.

 

[Just.Snaz]

if you draw a graph with a stationary point and draw a tangent at the point, it's horizontal so the gradient is zero. that's why you make x'=0 for stationary points.

I don't know/can't explain for x''..

 

[crammy90]

ahk fairs enuf
hows about when we do that for maximum and minimum volumes...what does x'=o for?

 

[Just.Snaz]

same thing? if y is your volume then x is your measurement.
For e.g. V = pi.r^2.h - for the volume of a cylinder. Now here you'd either get h in terms of r or r in terms of h. Say you get h in terms of r. You're y here is your V while your x is the r.

So if you think about graphing the equation for the volume, your maximum point is where your y is max, ie, your volume is maximum.