MAT136H1 Lecture Notes - Polar Coordinate System
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MAT136H1 Full Course Notes
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Question #3 (medium): concavity based on the 2nd derivative of parametric equations. When the second derivative is positive, it is concave up; and when the second derivative is negative, it is concave down. Given for parametric equations, its second derivative is given by. Notice the numerator where derivative of is taken with respect to parameter , while it is still divided by. Once the expression for second derivative is obtained, determine the possible values for where it distinguishes between concavity up and down. Sample question and determine for what value of parameter t is the curve concave upward? and. In order to check concavity, second derivative is needed. First calculate the first derivative ( ) and.
