ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 18 Oct 2010 14:35:37 +0200GRE Math Subject Test Sample Question #2https://ask.sagemath.org/question/7496/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
Mon, 18 Oct 2010 13:15:30 +0200https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/Comment by John Palmieri for <p>Find the linear equation for the line which touches the following curve only once when x = 0, curve: y - x = e^x</p>
https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/?comment=22557#post-id-22557I 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.Mon, 18 Oct 2010 14:08:11 +0200https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/?comment=22557#post-id-22557Comment by ccanonc for <p>Find the linear equation for the line which touches the following curve only once when x = 0, curve: y - x = e^x</p>
https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/?comment=22556#post-id-22556Yes, "touches" means "is tangent to", and sometimes tangents will touch curves more than at the point of interest. How should I change the text?Mon, 18 Oct 2010 14:35:37 +0200https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/?comment=22556#post-id-22556Answer by Mike Hansen for <p>Find the linear equation for the line which touches the following curve only once when x = 0, curve: y - x = e^x</p>
https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/?answer=11740#post-id-11740As 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][1]
[1]: /upfiles/12874221898800997.pngMon, 18 Oct 2010 14:17:07 +0200https://ask.sagemath.org/question/7496/gre-math-subject-test-sample-question-2/?answer=11740#post-id-11740