# Slope of a Curve

• Nov 14th 2012, 12:04 PM
spyder12
Slope of a Curve
• Nov 14th 2012, 12:12 PM
Plato
Re: Slope of a Curve
Quote:

Originally Posted by spyder12

Can you do the algebra?

$\frac{\frac{1}{h+16}-\frac{1}{16}}{h}=~?$
• Nov 14th 2012, 12:14 PM
MarkFL
Re: Slope of a Curve
$f(6+h)=\frac{1}{(6+h)+10}=\frac{1}{h+16}$

$f(6)=\frac{1}{(6)+10}=\frac{1}{16}$

Now, putting these into the quotient gives you what?
• Nov 14th 2012, 12:28 PM
spyder12
Re: Slope of a Curve
ok so then that equals (1/h) / h right? then what do i do
• Nov 14th 2012, 12:41 PM
skeeter
Re: Slope of a Curve
Quote:

Originally Posted by spyder12
ok so then that equals (1/h) / h right? then what do i do

$\frac{\frac{1}{h+16} - \frac{1}{16}}{h} \ne \frac{\frac{1}{h}}{h}$

you first need to combine the fractions in the numerator using the common denominator $16(h+16)$
• Nov 14th 2012, 12:42 PM
MarkFL
Re: Slope of a Curve
No, how did you get that?
• Nov 14th 2012, 12:46 PM
skeeter
Re: Slope of a Curve
Quote:

Originally Posted by MarkFL2
No, how did you get that?

methinks some creative algebra ...

$\frac{1}{h+16} = \frac{1}{h} + \frac{1}{16}$

... which, of course, is incorrect.
• Nov 14th 2012, 12:59 PM
MarkFL
Re: Slope of a Curve
That was my inclination as well...many folks make this kind of error. :)
• Nov 14th 2012, 06:58 PM
spyder12
Re: Slope of a Curve
alright so then ( (1) / 16(h+16) ) / h = ( (1) / (16h+265) ) / h = (16h+256)^-1 / h , so to answer my question a= 16 & b=256
• Nov 14th 2012, 07:00 PM
MarkFL
Re: Slope of a Curve
Yes, good work! :)
• Nov 15th 2012, 04:32 AM
skeeter
Re: Slope of a Curve
Quote:

alright so then ( (1) / 16(h+16) ) / h = ( (1) / (16h+265) ) / h = (16h+256)^-1 / h , so to answer my question a= 16 & b=256
you may have "stumbled" onto the correct constants, but this is incorrect

$\frac{1}{h} \left(\frac{1}{h+16} - \frac{1}{16}\right)$

$\frac{1}{h} \left(\frac{16}{16(h+16)} - \frac{h+16}{16(h+16)}\right)$

$\frac{1}{h} \left(\frac{16 - h - 16}{16(h+16)}\right)$

$\frac{1}{h} \left(\frac{ -h}{16(h+16)}\right)$

$\frac{ -1}{16(h+16)}\right) = \frac{-1}{16h + 256}$
• Nov 15th 2012, 12:02 PM
MarkFL
Re: Slope of a Curve
Good catch, I only looked at the end result.