Page 1 of 1

Question 23 of GR0568

Posted: Fri Oct 30, 2009 1:56 pm
by bonaluram
Hello,

The question is : For what value of b is the line y=10x tangent to the curve y=e^(bx) at some point in the x-y plane?

a) 10/e
b) 10
c) 10e
d) e^10
e) e

The correct answer is a.

I know that the derivative of the curve should be equal to the line however i couldn't make it. I would be very grateful to your help.

Thank you.

Re: Question 23 of GR0568

Posted: Fri Oct 30, 2009 2:09 pm
by mag487
You want to solve the system:

e^(bx) = 10x
b*e^(bx) = 10.

Dividing the second equation by the first gives us b = 1/x. Plugging this back into the first equation yields e = 10x, so x = e/10, so b = 10/e.

Re: Question 23 of GR0568

Posted: Fri Oct 30, 2009 2:15 pm
by bonaluram
Thank you very much for your help :)
I was nearly going crazy!