LogicalApple
Challenge (calculus)
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LogicalApple
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LogicalApple
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For what value of b is the line y = 10x tangent to the curve y = e^(bx)?
N00bstyle
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@hartnn, what are your thoughts about it?
hartnn
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10 = be^(bx)
and maybe to find point of intersection, 10x = e^(bx)
still thinking further steps...
LogicalApple
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Medal is awaiting .. . :)
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Haha, screw the medal :P
LogicalApple
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Oh wait I wrote the wrong thing down.
I meant to write down what was in the attachment... one sec.
LogicalApple
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For what value of b is the line y = 5x tangent to the curve y = e^(bx)?
LogicalApple
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Same logic though.
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yeah, idd, phew :P
mathmate
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At the required point, e^(bx) has a slope of 10 =>
be^(bx) = 10.
We can solve for b using newton's method.
hartnn
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5 =be^(bx)
5x = e^bx
---> bx =1
---->5x = e^1
x= e/5
b = 5/e
LogicalApple
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You have demonstrated your ability. Medal earned!
hartnn
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lol thanks :)
LogicalApple
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Although I like the idea of using Newton's method.. Sometimes it doesn't work though.
mathmate
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I agree. There are known strict conditions of convergence. We need to get a close starting point. In any case, we can solve for b=5/e here, but still you need to calculate x one way or another.
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Good question btw, I like.
Now back to drinking beer.