Let r(t) (x(t), y(t)) trace a plane curve C Assume that x '(t 0 ) 0 Show that the slope of the tangent vector r(t 0 ) is equal to the slope dy dx of the curve at r(t 0 )

Question: Let r(t) = (x(t), y(t)) trace a plane curve C. Assume that x'(t 0 ) 0. Show that the slope of the tangent vector

Let r(t) = (x(t), y(t)) trace a plane curve C. Assume that x'(t₀) ≠ 0. Show that the slope of the tangent vector r(t₀) is equal to the slope dy/dx of the curve at r(t₀).

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