Question

Challenge (calculus)

Answer 1

For what value of b is the line y = 10x tangent to the curve y = e^(bx)?

Answer 2

@hartnn, what are your thoughts about it?

Answer 3

10 = be^(bx)
and maybe to find point of intersection, 10x = e^(bx)
still thinking further steps...

Answer 4

Medal is awaiting .. . :)

Answer 5

Haha, screw the medal :P

Answer 6

Oh wait I wrote the wrong thing down.
I meant to write down what was in the attachment... one sec.

Answer 7

For what value of b is the line y = 5x tangent to the curve y = e^(bx)?

Answer 8

Same logic though.

Answer 9

yeah, idd, phew :P

Answer 10

At the required point, e^(bx) has a slope of 10 =>
be^(bx) = 10.
We can solve for b using newton's method.

Answer 11

5 =be^(bx)
5x = e^bx
---> bx =1

---->5x = e^1
x= e/5
b = 5/e

Answer 12

You have demonstrated your ability. Medal earned!

Answer 13

lol thanks :)

Answer 14

Although I like the idea of using Newton's method.. Sometimes it doesn't work though.

Answer 15

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.

Answer 16

Good question btw, I like.
Now back to drinking beer.