Відео

The absolute maximum is 2 and the absolute minimum is -2. Note that these are y-values. If determining absolute minimum and maximum *points*, then the absolute maximum occurs at (-2, 2) and (1,2), and the absolute minimum occurs at (2, -2).

Vectors in component form are always measured in the same way as Cartesian coordinates, relative to the x- and y-axes. Bearings are always measured from the y-axis.

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This actually depends on the textbook. Some textbooks will include the far left/right endpoints for local extrema, and others don't. I based this video off of the Stewart Calculus text, which didn't include them. Check your text, or with your teacher, to know if you should include them in your considerations.

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Yes, that is correct.

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Great question! This means cot(2ϴ)=0, so ϴ=π/4

@@symplitmath why?, please may you explain further?

​@@rayaanrahman2888 Do you know what cot is? And at what angles does cot = 0? Look this up and review the double angle formulas and you should understand.

Fair point. I use the cursor to point to them, and the cursor isn’t the easiest to see, but it’s all the points near x=-3.

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Not yet, but I am open to suggestions and requests. Let me know specifics of what you'd like to see.

I think so too!

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If you want to think of this function as a transformation of the reciprocal function, you would need to write it in reduced form. If you do this, the function becomes f(x)=9-36/(x+4), and then you see the negative in front of the reciprocal function. I didn't graph the function with that process, but it is certainly a valid approach.

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This is the TI-Nspire, which is a pretty powerful calculator. I'm using the emulator software in this video.

I very long algebraic process of plugging in the conversions shown in this video (ua-cam.com/video/L3phw2wFWS4/v-deo.html) in the equation Ax^2+Bxy+Cy^2+Dx+Ey+F=0, leads us to the formula for the angle of rotation. It is a miserable algebraic exercise.

I think you are referring to the behavior of the middle section. It may look like a quadratic but it is not, because it follows those asymptotes. It has that shape because we know the function never crosses the x-axis (b/c the numerator is never zero. If you wanted a cubic-esque shape, it would have to cross the x-axis, but it can't!

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The common ratio is defined in a geometric sequence to be the ratio of outputs for consecutive integer inputs. Note that when the year increases by 1, the bacteria is multiplied by 4.

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This solution does not place the problem on a Cartesian plane, but rather uses vectors to solve it. However, vectors are already Cartesian in nature, so in a sense you could think of it as a Cartesian solution.

This is the Notability desktop app for Mac.

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Nice addition! Thanks!

@@symplitmath Did not realize that I get a compliment from the creator. No problem. I thoroughly enjoyed this video.

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Here you go: drive.google.com/file/d/1xO0n_Y-jntHeVUzpPfwOv5HrQ4Pqr3Dq/view?usp=share_link

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