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.

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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.

Mathematics
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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?
HI!!
for a line, derivative = slope

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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?
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
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 \[\frac{f(a+h)-f(a)}{h}\]?
Number 2!
ok so first replacing \(x\) by \(2\) we have \[\frac{f(2+h)-f(2)}{h}\]
in this case \[f(x)=5x+9\] so \[f(2)=5\times 2+9=19\]
When plugging it in isn't it supposed to look like this?:\[\frac{ (5(x+h)+9)-(5x+9) }{ h }\]
it is if you use x instead of 2
since it makes no difference lets do it your way
Oh, okay. I didn't realize you could plug in 2 right away - I just always did it at the end
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
you can almost do it in your head \[5x+5h+9-5x-9=5h\]
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
lol your welcome \[\color\magenta\heartsuit\]

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