Finding the Slope of a Tangent Line to f(x) at (2,3)

[fitz_calc]

Homework Statement

the line tangent to the graph of f(x) = x-1/x at (2,3) has what slope?

The Attempt at a Solution

Same story with this problem, I remember doing it but can't remember how to attack the problem. can someone give me a good first step to go off of?

 

[HallsofIvy]

The slope of the tangent line to a curve, at any point, is the value of the derivative their. That's often taken as a definition of derivative. In order to differentiate, I would write that as f(x)= x- x^-1.

 

[fitz_calc]

1 + 1/4 = 5/4, gotcha.

so the 3/2 on the y-axis has no role in determining the final answer?

 

[Office_Shredder]

Of minor note, the graph doesn't actually pass through (2,3), but I'll assume it's a typo (though it would be a mean trick question)

The value of f(x) is pretty much irrelevant to the slope of the tangent line, yes. (in fact, note you can add any constant to f, making it f(x)+c, and it will still have the same derivative.)