Wed, 20 Feb 2008 23:56:43 -0600 from OP
<facetious_nickname@[EMAIL PROTECTED]
>:
> On p. 58 & 59 of Spivak's Calculus, he says "Given two distinct
> points (a,b) and (c,d), find the linear function f whose graph goes
> through (a,b) and (c,d). This amounts to saying that f(a) = b and
> f(c) = d. If f is to be of the form f(x) = Aa + B, then we must have:
>
> Aa + B = b;
> Ac + B = d;
>
> therefore A = (d - b)/(c - a) and B = b - [(d - b)/(c - a)]a, so [etc.]"
>
> I substituted A for the alpha symbol and B for the beta symbol. My
> question is, why "therefore"? How does he pull the values of A and B
> out of those two equations?
They're simultaneous equations in A and B, so solve them like any
other simultaneous equations. Can you solve these:
3A + B = 11
A - 2B = -15
Follow exactly the same steps to solve your two.
And, meaning no disrespect, if you can't solve the two equations I
gave, you need to study algebra before attempting calculus.
(By the way, I've dipped into Spivak's book, and while it's good I
think it's considerably harder than the typical undergrad calculus
book. If you're doing this for self study you might want a book that
is paced a little slower.)
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
A: Maybe because some people are too annoyed by top posting.
Q: Why do I not get an answer to my question(s)?
A: Because it messes up the order in which people normally read text.
Q: Why is top posting such a bad thing?
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