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Yogi
Posts:
323
Registered:
12/6/04


Re: Precalc
Posted:
Sep 8, 2004 12:10 PM


On 8 Sep 04 09:32:15 0400 (EDT), jeremy wrote: >I haven't taken math since high scool and I forgot everything, can >someone please explain this problem for me.(Difference quotient) > >f(x)= 2x+5
The only statement of the problem is the two words "Difference quotient"! The difference quotient for a function f(x) is the fraction (quotient) formed of the difference (f(x) f(a))/(xa) or sometimes (f(b)f(a))/(ba). Unfortunately, you have given us neither a nor b!
For this particular example, it doesn't matter. Since this is a "linear function", the difference quotient for any a, b (or any a, x) is a constant: the slope.
Taking a to be any number, f(a)= 2a+ 5. Taking b to be any number, f(b)= 2b+ 4. f(b) f(a)= (2b+5) (2a+ 5)= (2b2a)+ (55)= 2(ba). That's the numerator of the difference quotient. The denomiator is ba so: (f(b) f(a))/(ba)= 2(ba)/(ba)= 2 (as long as b is not equal to a).



