## CalleyLeeAnn one year ago Find the derivative of f(x) = 5x + 9 at x = 2. I know this question has already been asked, but I don't understand the other answers.

1. CalleyLeeAnn

Using the difference quotient, I get 0, but other sources tell me the answer is 5. How do I get the right answer using the difference quotient?

2. misty1212

HI!!

3. misty1212

for a line, derivative = slope

4. misty1212

we can use the :"difference quotient" if you like, it is the change in y over the change in x , which is still the slope you need the steps?

5. CalleyLeeAnn

Let's use the difference quotient please :) And yes, let's go over the steps because I'm obviously doing something wrong with it lol

6. misty1212

ok first of all, the "at x = 2" part is unnecessary because the slope of a line is a constant, and therefore does not depend on the number but since that is what it says, lets go ahead and use it are you using $\frac{f(x)-f(a)}{x-a}$ or $\frac{f(a+h)-f(a)}{h}$?

7. CalleyLeeAnn

Number 2!

8. misty1212

ok so first replacing $$x$$ by $$2$$ we have $\frac{f(2+h)-f(2)}{h}$

9. misty1212

in this case $f(x)=5x+9$ so $f(2)=5\times 2+9=19$

10. CalleyLeeAnn

When plugging it in isn't it supposed to look like this?:$\frac{ (5(x+h)+9)-(5x+9) }{ h }$

11. misty1212

it is if you use x instead of 2

12. misty1212

since it makes no difference lets do it your way

13. CalleyLeeAnn

Oh, okay. I didn't realize you could plug in 2 right away - I just always did it at the end

14. misty1212

lets do it your way anyway it is pretty easy since all you have to do is some algebra in the numerator multiply out and combine like terms

15. misty1212

you can almost do it in your head $5x+5h+9-5x-9=5h$

16. CalleyLeeAnn

Wow, I just realized my mistake lol.I forgot to divide by h at the end and that totally threw me off! Thanks so much for your help :D

17. misty1212

lol your welcome $\color\magenta\heartsuit$