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
1 Answer
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.
Your Answer
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Asked: 14 years ago
Seen: 611 times
Last updated: Oct 18 '10
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?