CalleyLeeAnn
  • CalleyLeeAnn
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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SOLVED
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schrodinger
  • schrodinger
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CalleyLeeAnn
  • 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?
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
for a line, derivative = slope

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misty1212
  • 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?
CalleyLeeAnn
  • 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
misty1212
  • 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 \[\frac{f(a+h)-f(a)}{h}\]?
CalleyLeeAnn
  • CalleyLeeAnn
Number 2!
misty1212
  • misty1212
ok so first replacing \(x\) by \(2\) we have \[\frac{f(2+h)-f(2)}{h}\]
misty1212
  • misty1212
in this case \[f(x)=5x+9\] so \[f(2)=5\times 2+9=19\]
CalleyLeeAnn
  • CalleyLeeAnn
When plugging it in isn't it supposed to look like this?:\[\frac{ (5(x+h)+9)-(5x+9) }{ h }\]
misty1212
  • misty1212
it is if you use x instead of 2
misty1212
  • misty1212
since it makes no difference lets do it your way
CalleyLeeAnn
  • CalleyLeeAnn
Oh, okay. I didn't realize you could plug in 2 right away - I just always did it at the end
misty1212
  • 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
misty1212
  • misty1212
you can almost do it in your head \[5x+5h+9-5x-9=5h\]
CalleyLeeAnn
  • 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
misty1212
  • misty1212
lol your welcome \[\color\magenta\heartsuit\]

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