Question

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.

Answer 1

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?

Answer 2

HI!!

Answer 3

for a line, derivative = slope

Answer 4

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?

Answer 5

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

Answer 6

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
\[\frac{f(a+h)-f(a)}{h}\]?

Answer 7

Number 2!

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

it is if you use x instead of 2

Answer 12

since it makes no difference lets do it your way

Answer 13

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

Answer 14

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

Answer 15

you can almost do it in your head
\[5x+5h+9-5x-9=5h\]

Answer 16

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

Answer 17

lol your welcome
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