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How to minimize and maximize equations?

My questions ask me to find the shortest distance from the origin to the curve, and the maximum distance and my notes say that to do this I need to "minimize" the distance and "maximize" the distance. What does this mean and how do I do this?
Original post by Farhan.Hanif93


D=x2+(f(x))2D=x^2+(f(x))^2.



Pythagoras has clearly changed since my day :holmes:
Original post by ghostwalker
Pythagoras has clearly changed since my day :holmes:

On second thought, I wasn't being quite as stupid as it first seemed. What I meant to say was this:

The distance of the point (x,f(x))(x,f(x)), which lies on the curve y=f(x)y=f(x), from the origin is given by D=x2+(f(x))2D=\sqrt{x^2 + (f(x))^2}. Which is max or min iff x2+(f(x))2x^2+(f(x))^2 is max or min. So differentiation of that expression w.r.t. x and setting equal to zero will provide you with the points on the curve that are maximum or minimum distance away from the origin.

Should have made it clearer what I meant the first time. :p:
Original post by Farhan.Hanif93


Should have made it clearer what I meant the first time. :p:


Nice footwork :p:
Original post by ghostwalker
Nice footwork :p:

After stating the wrong formula for pythagorus :sigh:, I really did have to do something about it. :wink:
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Original post by Farhan.Hanif93
So differentiation of that expression w.r.t. x and setting equal to zero will provide you with the points on the curve that are maximum or minimum distance away from the origin.

Just to be clear to "claret and blue" about why you're doing this:
Differentiating something with respect to x means "finding out how fast something changes as you change x."

You want to set the answer to zero because at a minimum (or maximum) point, the function isn't changing with respect to x. If you have trouble understanding why this is so, think of a hill: At the highest point the hill will be flat, if it wasn't flat you could walk uphill a bit more and get even higher

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