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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.
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.

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CalleyLeeAnn
 one year ago
Best ResponseYou've already chosen the best response.0Using 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?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1for a line, derivative = slope

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1we 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?

CalleyLeeAnn
 one year ago
Best ResponseYou've already chosen the best response.0Let's use the difference quotient please :) And yes, let's go over the steps because I'm obviously doing something wrong with it lol

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1ok 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 \[\frac{f(x)f(a)}{xa}\] or \[\frac{f(a+h)f(a)}{h}\]?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1ok so first replacing \(x\) by \(2\) we have \[\frac{f(2+h)f(2)}{h}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1in this case \[f(x)=5x+9\] so \[f(2)=5\times 2+9=19\]

CalleyLeeAnn
 one year ago
Best ResponseYou've already chosen the best response.0When plugging it in isn't it supposed to look like this?:\[\frac{ (5(x+h)+9)(5x+9) }{ h }\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1it is if you use x instead of 2

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1since it makes no difference lets do it your way

CalleyLeeAnn
 one year ago
Best ResponseYou've already chosen the best response.0Oh, okay. I didn't realize you could plug in 2 right away  I just always did it at the end

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1lets 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

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1you can almost do it in your head \[5x+5h+95x9=5h\]

CalleyLeeAnn
 one year ago
Best ResponseYou've already chosen the best response.0Wow, 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

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1lol your welcome \[\color\magenta\heartsuit\]
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