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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
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@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
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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

2 Answers 2

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

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3  
How do you find the slope of the tangent line? –  The Chaz 2.0 Jul 7 '13 at 15:57

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