# GRE Math Subject Test Sample Question #2

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

GRE Math Subject Test Sample Question #2

1

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 $y = 2x + 1$.

Asked: **
2010-10-18 06:15:30 -0500
**

Seen: **403 times**

Last updated: **Oct 18 '10**

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.

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.

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?