## LogicalApple 2 years ago Challenge (calculus)

1. LogicalApple

2. LogicalApple

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

3. N00bstyle

4. hartnn

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

5. LogicalApple

Medal is awaiting .. . :)

6. N00bstyle

Haha, screw the medal :P

7. LogicalApple

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

8. LogicalApple

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

9. LogicalApple

Same logic though.

10. N00bstyle

yeah, idd, phew :P

11. mathmate

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

12. hartnn

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

13. LogicalApple

You have demonstrated your ability. Medal earned!

14. hartnn

lol thanks :)

15. LogicalApple

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

16. mathmate

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.

17. N00bstyle

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