For what value of t is the slope of the curve undefined for the graph

Question

 

For what value of t is the slope of the curve undefined for the graph defined by x = 8 - t³, y = t² - 6t?

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Answer 1

x = 8 - t³ and y = t² - 6t

dy/dx = (dy/dt) / (dx/dt) = (2t - 6) / (-3t²) = slope of tangent

dy/dx is undefined when -3t² = 0. So, t = 0.

Point where dy/dx is undefined is (x,y) where x = 8-0³ = 8 and y = 0² - 6(0) = 0