# Which of the following is not used to determine the slope of a function algebraically?

I dont know the answer to the above question. I think it is the slope of a secant line but I'm not sure

a. slope of a secant line
b. graphing calculator
c. difference quotient
d. rationalizing numerator

-
@AndreasCaranti, possibly the "rationalizing" of the numerator is in the context of finding the derivative of $\sqrt x$, for example. See here:sosmath.com/calculus/diff/der01/der01a.html – The Chaz 2.0 Jul 7 '13 at 15:52
@TheChaz2.0 Hadn't thought of that, thanks, you're quite right. Deleting comment. So it's the graphing calculator? – Andreas Caranti Jul 7 '13 at 15:53
That's my best guess. I'm not overly impressed with this question, to say the least... – The Chaz 2.0 Jul 7 '13 at 15:56
@TheChaz2.0, I agree. – Andreas Caranti Jul 7 '13 at 16:01

All of the given options can actually be used to find the slope of a function:

1. The slope of the secant line is the difference quotient.
2. A good graphing calculator (e.g. TI-89 or HP-50G) can find it algebraically.
3. Taking the limit of the difference quotient gives the slope of the function.
4. Rationalizing the numerator could be done as part of taking a limit (e.g. this example from the comments.)
-

Your guess is true!
a. slope of a secant line
actually slope of tangent line determines slope of a function

-
How do you find the slope of the tangent line? – The Chaz 2.0 Jul 7 '13 at 15:57