Unit II: Lec 7 | MIT Calculus Revisited: Single Variable Calculus

Unit II: Lecture 7: Curve Plotting

Instructor: Herb Gross

View the complete course: http://ocw.mit.edu/RES18-006F10

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Category:

Education

Tags:

• calculus
• single variable
• sets
• functions
• derivatives
• limits
• differentiation
• circular functions
• definite integral
• transcendental functions
• integration
• infinite series

[anakmudajaman]

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[AntoMelta]

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[willamricard]

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[imegatrone]

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[bundawartini]

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[shadowC10ne]

I'm ashamed to admit I never realized that functions of bigger powers like x^4 were more tangent to the x-axis than function x near 0. I always assumed the bigger the power - the sharper the rise (everywhere).

However, professor Gross did mention that after |x| > 1 functions of higher powers rise more sharply at 29:20.

I think if there would be 1 and -1 on the x-axis to indicate that the graph function is still close to 0 there would be less confusions.

[hgross3comcast]

@VVillowz No need to apologize. In fact I was pleased that you were observant enough to detect something that might have confused others. I was intent in showing that even though the x-axis was tangent to both y == x^2 and y = x^4 at (0,0), the curve y = x^4 “hugged” the x-axis longer than the curve y = x^2. However I neglected to indicate that once |x| > 1, the curve y = x^4 rises much more rapidly than the curve y = x^2. Feel free to write to me at hgross3@comcast.net

[hgross3comcast]

@VVillowz Yes! What sometimes happens when you are too focused on a particular point (in this case, the meaning of higher order derivatives), you are sometimes obivious to errors on the periphery. That is, I wasn't focusing on what the curves actually looked like other than they all were "bowl shaped"".

[VVillowz]

@hgross3comcast Oh, I understand. You thought that I was pointing out Gross saying that the curves would intersect somewhere else beyond the points x=0 and x=1. I was only referring to the mislabeling of the curves at 28:20; but indeed you are correct too. Gross it seems confused himself with his astounding use of language to elucidate mathematical concepts.

The fact that you didn't catch the error must mean that you understand with or without mistakes being made on the board.

[hgross3comcast]

@VVillowz The way the curves are drawn in my lecture they do not seem to intersect any where other than at the origin.. Yet no matter how they are labeled both curves must pass through (-1,1) and (1,1)... or are you referring to something else that I've said?