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LogicalApple
 2 years ago
Challenge (calculus)
LogicalApple
 2 years ago
Challenge (calculus)

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LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1For what value of b is the line y = 10x tangent to the curve y = e^(bx)?

N00bstyle
 2 years ago
Best ResponseYou've already chosen the best response.0@hartnn, what are your thoughts about it?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.110 = be^(bx) and maybe to find point of intersection, 10x = e^(bx) still thinking further steps...

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1Medal is awaiting .. . :)

N00bstyle
 2 years ago
Best ResponseYou've already chosen the best response.0Haha, screw the medal :P

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1Oh wait I wrote the wrong thing down. I meant to write down what was in the attachment... one sec.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1For what value of b is the line y = 5x tangent to the curve y = e^(bx)?

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1Same logic though.

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0At the required point, e^(bx) has a slope of 10 => be^(bx) = 10. We can solve for b using newton's method.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.15 =be^(bx) 5x = e^bx > bx =1 >5x = e^1 x= e/5 b = 5/e

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1You have demonstrated your ability. Medal earned!

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.1Although I like the idea of using Newton's method.. Sometimes it doesn't work though.

mathmate
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

N00bstyle
 2 years ago
Best ResponseYou've already chosen the best response.0Good question btw, I like. Now back to drinking beer.
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