Ask Your Question
0

GRE Math Subject Test Sample Question #2

asked 2010-10-18 06:15:30 -0600

ccanonc gravatar image

updated 2011-05-12 09:09:24 -0600

Kelvin Li gravatar image

Find the linear equation for the line which touches the following curve only once when x = 0, curve: y - x = e^x

edit retag flag offensive close merge delete

Comments

I don't think this question makes sense, unless you clarify what "touches" means. If it just means "intersects", then any line with slope less than 1 through the point (0,1) should work. If it means "is tangent to", then you can use Sage to find the derivative at x=0, etc.

John Palmieri gravatar imageJohn Palmieri ( 2010-10-18 07:08:11 -0600 )edit

Yes, "touches" means "is tangent to", and sometimes tangents will touch curves more than at the point of interest. How should I change the text?

ccanonc gravatar imageccanonc ( 2010-10-18 07:35:37 -0600 )edit

1 answer

Sort by ยป oldest newest most voted
1

answered 2010-10-18 07:17:07 -0600

Mike Hansen gravatar image

updated 2010-10-18 07:17:52 -0600

As John said,

sage: f = e^x + x
sage: plot(f, x, -1, 1)
sage: diff(f, x).subs(x=0)
2
sage: f.subs(x=0)
1
sage: g = 2*x + 1
sage: plot(f, x, -2, 2) + plot(g, x, -2, 2, color='red')

The line is $y = 2x + 1$.

Plot of e^x+x and 2*x+1

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2010-10-18 06:15:30 -0600

Seen: 388 times

Last updated: Oct 18 '10