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Question about parametric equations

Given two parametric equations and the t range, when asked to find the minimum/maximum x values is it always okay to just substitute the upper and lower end of the given t range? But what if the p(t) graph is not always increasing, wouldn’t this mean the graph “goes back on itself”. Sorry for confusing phrasing, thank you.
Original post by anon_ymous123
Given two parametric equations and the t range, when asked to find the minimum/maximum x values is it always okay to just substitute the upper and lower end of the given t range? But what if the p(t) graph is not always increasing, wouldn’t this mean the graph “goes back on itself”. Sorry for confusing phrasing, thank you.


Just sketch/reason about x(t). Sometimes the min/max values will be at the ends, though there is no reason to assume that and generally the function x(t) isnt that complex.

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