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Help with math


kdani

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The X ^ 2 + 9 function moved tangent.

At which point should the tangent be moved so that the tangent length between the launch point and the X axis is minimal?

my way:

I calculated the tangent equation from the slope (derived), and the point (x, x ^ 2 + 9) and found the tangent point of the tangent with the X-axis.

Then Pythagoras, and this should cut and find a minimum extreme point.

But it does not work out ....

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It came out of an equation from the fourth degree ... The point on the x-axis was X ^ 2-9 (/ 2X) and the second point is x, x ^ 2 + 9,

Pythagoras on this thing comes out really ugly .... and the derivative is reset to me in X = 0 that does not make sense (at this point the distance is actually maximal ....)

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It seems to me enough to make a derivative and compare it to zero (ie extreme point), the second derivative is 2 (greater than 0, ie minimum).

It has been proven that this is a launch point and that it is a minimum, from the placement we got a positive y (9) => but the original equation is always positive => and because it is a minimum, it is the point closest to the x-axis.

Perhaps it is possible to improve by the fact that such a equation is smiling and has a single minimum and start with it.

If for example this function was x ^ 2-9, then it would be more complicated because it has points below the x-axis.

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Of course 0 is the right answer. Think for a moment ...

Or if you or I did not understand the question ... If you are asked how long the tangent between the launch point and its cutting with the x axis you must know that 0 is the farthest answer, where the length is infinite (x does not reset throughout the entire range).

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Or if you or I did not understand the question ... If you are asked how long the tangent between the launch point and its cutting with the x axis you must know that 0 is the farthest answer, where the length is infinite (x does not reset throughout the entire range).

Yes, I looked over and realized something else.

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