# Thread: Slope of a Curve

1. ## Slope of a Curve

Let f(x) be the function . Then the quotient can be simplified to for: a= _____ & b= _____

2. ## Re: Slope of a Curve

Originally Posted by spyder12
Let f(x) be the function . Then the quotient can be simplified to for: a= _____ & b= _____
Can you do the algebra?

$\frac{\frac{1}{h+16}-\frac{1}{16}}{h}=~?$

3. ## 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?

4. ## Re: Slope of a Curve

ok so then that equals (1/h) / h right? then what do i do

5. ## Re: Slope of a Curve

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 $16(h+16)$

6. ## Re: Slope of a Curve

No, how did you get that?

7. ## Re: Slope of a Curve

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.

8. ## Re: Slope of a Curve

That was my inclination as well...many folks make this kind of error.

9. ## 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

10. ## Re: Slope of a Curve

Yes, good work!

11. ## 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
you may have "stumbled" onto the correct constants, but this is incorrect

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

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

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

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

$\frac{ -1}{16(h+16)}\right) = \frac{-1}{16h + 256}$

12. ## Re: Slope of a Curve

Good catch, I only looked at the end result.