just draw several position vectors vk, for i=1..n, getting closer to the vector at the given point, r. For each vk, draw vk-r. These serve the same purpose as secants in the usual x-y plots illustrating the approach to a tangent.
Pick up any good book on vector analysis and you will find such illustrations. Also, as always, google is your friend.
Show a graphical method of approximating the instantaneous rate of change at x = 3 for the function ƒ(x) = -x2 + 4x + 1 using secants. Show two graphical approximations.
I had the same question but instructed to find it using a numerical method.
No problem with that, but Im not sure how to calculate graphically.
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Shoot. I see that you were in fact just talking about an x-y plot. Pick any point P on the curve, and several nearby points, qk. Draw the secants to the various points. You can see that as qk approaches P, the secant is ever more nearly a tangent.
I'm sure your textbook has this very illustration, maybe for some other f(x).
I'm sure your textbook has this very illustration, maybe for some other f(x).
1 answer