Question on the graphical proof of the Product Rule. It's on the unit 1 sept 08 lecture note. It is not on the accompanying notes. I downloaded the professor's entire lecture note at this website

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/lecture-notes/

if you want to check it out but I'll try to draw the picture below. It's with rectangles.

Question

Question on the graphical proof of the Product Rule. It's on the unit 1 sept 08 lecture note. It is not on the accompanying notes. I downloaded the professor's entire lecture note at this website

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/lecture-notes/

if you want to check it out but I'll try to draw the picture below. It's with rectangles.

anonymous · Answer

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My question is in the explanation of the graphical proof. It says that $$\Delta u = u(x+\Delta x) - u(x)$$

I'm having a hard time "seeing" the picture because the way I understood is that u(x) is some y-coordinate. How does that graphically make sense? 

I get that they're trying to show that $$\Delta u = (u + \Delta u) - u$$
So wouldn't the x-axis line just be $$\ u + \Delta u$$