Curve Sketching with Asymptotes x/(x - 2)^2 and Derivatives of Rational Function

Understand algorithm for curve sketching using derivatives
Practice Video: • Calculus Curve Sketchi...
15 Multiple Choice and 7 Communication Thinking Questions on Increasing Decreasing and Curve Sketching. IB AP Calculus students can practice without Calculator.
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Critical number is the point where the derivative is zero or undefined. Maximum occurs where the derivative changes from positive to negative. Minimum is at the point where the first derivative changes from negative to positive increasing to decreasing. Minimum is at a point where the derivative changes from decreasing to increasing. Second derivative can be used to confirm maximum or minimum at the critical point. Positive second derivative means minimum and negative means maximum.
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[@HATL201]

Excellent lecture. However I didn't get why you replaced 100 and -100 to check the behaviour of the graph in-terms of horizontal asymptote? For vertical asymptote, we replaced 1.9 and 2.1 , so why didn't we replace 0.1 and -0.1 for the horizontal asymptote?

[@alexbabich2698]

He's just picking x values at those locations to see what the y values are. 0.1 and -0.1 would be good if there was a vertical asymptote at x=0

[@George-Smith]

Please why did you not expand the denominator

[@arcyaquino6402]

How did you get the critical number -4 and 2

[@naturefirst9174]

Very well explained Thank you sir

[@ginevrabianco4056]

How do you know what the y interept is also the x intercept? (0,0)?

[@MathematicsTutor]

If x = 0 you get y = 0. So Origin is both x- and y-intercept. Hope that is clear. Thanks

[@kartikchauhan5039]

Helpful video 👍

[@jaymaabharte.6421]

Thanks sir . 👍❤️

[@mintchilled406]

this helped me with my unit 7 test!

[@mulxmak]

👍👍

[@kalamkavi7866]

Thankyou so much sir

[@jameyatesmauriat6116]

This to me is hard