If the tangent is horizontal, it is where the tangent is zero. In single var. calc. that would be at max. or min. for example. I am confused about what horizontal tangent refers to when I am given a parametric equation.
E.g. At what value of t does x=t^2 -t and y=t^2 +t have a horizontal tangent?
The answer is -1/2 which can be found by setting y'=0. I don't understand why this happens though. As in, why dy/dt rather than dy/dx or why does dx/dt not apply? In describing the curve, what is the relationship between the two (x and y given in parametric form) that I could just only look at dy/dt?
My first instinct was to look for dy/dx which would look something like (2t+1)/(2t-1).
E.g. At what value of t does x=t^2 -t and y=t^2 +t have a horizontal tangent?
The answer is -1/2 which can be found by setting y'=0. I don't understand why this happens though. As in, why dy/dt rather than dy/dx or why does dx/dt not apply? In describing the curve, what is the relationship between the two (x and y given in parametric form) that I could just only look at dy/dt?
My first instinct was to look for dy/dx which would look something like (2t+1)/(2t-1).
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