Newton's Difference Quotient

[stinajeana]

f(x)=1/2x-7, a=3

... use Newton's Difference Quotient to calculate f'(a), then find the equation of the tangent line to the graph of f at x=a

 

[stapel]

f(x)=1/2x-7

What you have posted means something like this:

. . . . .\(\displaystyle f(x)\, =\, \frac{1}{2x}\, -\, 7\)

Is that what you meant? Or is the function maybe more like this:

. . . . .\(\displaystyle f(x)\, =\, \frac{1}{2x\, -\, 7}\)

... use Newton's Difference Quotient....

There are at least two different versions of this Quotient. Which is your book using?

Thanks!

 

[stinajeana]

Hello!
I mean't the second equation. Sorry for the confusion

 

[lookagain]

Hello!
I mean't the second equation. Sorry for the confusion

stinajeana,

you admitted to it being the second equation. I'll give a third choice to ponder.

Instead, could it have been \(\displaystyle \ f(x) \ = \ \dfrac{1}{2}x - 7 \ ?\)

 

[HallsofIvy]

As stapel said in his first response, there are at least two different forms of "Newton's difference quotient", for function f(x) at x= a. They are:

i) \(\displaystyle \frac{f(a+h)- f(a)}{h}\)
and

ii) \(\displaystyle \frac{f(x)- f(a)}{x- a}\)

But the real question is, "why haven't you at least tried this problem yourself?". If you had we would know which you meant.