Question 23 of GR0568

Forum for the GRE subject test in mathematics.
bonaluram
Posts: 7
Joined: Fri Oct 30, 2009 1:51 pm

Question 23 of GR0568

Postby bonaluram » Fri Oct 30, 2009 1:56 pm

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.

mag487
Posts: 13
Joined: Thu Aug 06, 2009 3:59 am

Re: Question 23 of GR0568

Postby mag487 » Fri Oct 30, 2009 2:09 pm

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.

bonaluram
Posts: 7
Joined: Fri Oct 30, 2009 1:51 pm

Re: Question 23 of GR0568

Postby bonaluram » Fri Oct 30, 2009 2:15 pm

Thank you very much for your help :)
I was nearly going crazy!




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