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Robert Israel

6577 Reputation

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18 years, 213 days
University of British Columbia
Associate Professor Emeritus
North York, Ontario, Canada
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These are replies submitted by Robert Israel

No...

Robert Israel 6577
December 04 2007
0 0
What does it mean for a line to be tangent to a curve at a point?

No...

Robert Israel 6577
December 04 2007
What does it mean for a line to be tangent to a curve at a point?

Part of it...

Robert Israel 6577
December 04 2007
0 0
You have one of the conditions. Now something about the derivative?

Part of it...

Robert Israel 6577
December 04 2007
You have one of the conditions. Now something about the derivative?

Try again...

Robert Israel 6577
December 04 2007
0 0
Let's start with one of the points. What do you know about the equation of the tangent line to the curve at x = x1?

Try again...

Robert Israel 6577
December 04 2007
Let's start with one of the points. What do you know about the equation of the tangent line to the curve at x = x1?

What you need...

Robert Israel 6577
December 03 2007
0 0
OK, so if your curve is y = f(x) and the tangent line is y = a*x+b, what equations say that the line is tangent to the curve at x=x1 and at x=x2?

What you need...

Robert Israel 6577
December 03 2007
OK, so if your curve is y = f(x) and the tangent line is y = a*x+b, what equations say that the line is tangent to the curve at x=x1 and at x=x2?

Explanation...

Robert Israel 6577
December 03 2007
0 0
Perhaps a picture would help: Is this the situation you're interested in?

Explanation...

Robert Israel 6577
December 03 2007
Perhaps a picture would help: Is this the situation you're interested in?

has(..., I)...

Robert Israel 6577
December 03 2007
0 0
It first evaluates t numerically using evalf, then checks if the result "contains I", i.e. has a nonzero imaginary part. I put "contains I" in quotes because a complex float actually doesn't literally contain I in its internal representation, but "has" treats this as a special case. There may be a risk in some cases that a root that is actually real may appear to have a small imaginary part due to roundoff error, but that doesn't happen in this case.

has(..., I)...

Robert Israel 6577
December 03 2007
It first evaluates t numerically using evalf, then checks if the result "contains I", i.e. has a nonzero imaginary part. I put "contains I" in quotes because a complex float actually doesn't literally contain I in its internal representation, but "has" treats this as a special case. There may be a risk in some cases that a root that is actually real may appear to have a small imaginary part due to roundoff error, but that doesn't happen in this case.

An instructor...

Robert Israel 6577
December 03 2007
0 0
Yes, I am in the Mathematics Department at University of British Columbia.

An instructor...

Robert Israel 6577
December 03 2007
Yes, I am in the Mathematics Department at University of British Columbia.

Which version of Maple?...

Robert Israel 6577
December 03 2007
0 0
It looks like the D operator is not working on p. Hmmm, I see that happens in Maple 9.5. Well, replace D(p)(x) by diff(p(x),x) and it should work.
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