The discussion focuses on finding the slope of a parametrized curve defined by the equations x3 + 2t2 = 9 and 2y3 - 3t2 = 4 at t = 2. The user correctly identifies the relationship dy/dx = (dy/dt)/(dx/dt) for parametrized curves and attempts to apply implicit differentiation. The solution involves calculating dy/dt and dx/dt, ultimately leading to the conclusion that dy/dx simplifies with t canceling out, providing a clear method for finding the slope.
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Find dx/dt in a similar fashion. Also find x & y, when t = 2.miglo said:Homework Statement
x^3+2t^2=9, 2y^3-3t^2=4, t=2
find the slope of the curve at the given value of t
Homework Equations
The Attempt at a Solution
i know dy/dx=(dy/dt)/(dx/dt) for parametrized curves
but how do i use implicit differentiation on parametrized curves?
i tried d/dt(2y^3-3t^2)=d/dt(4)
=6y^2*dy/dt-6t=0
=6y^2*dy/dt=6t
=dy/dt=t/y^2 ? but shouldn't dy/dt be defined in t's only? I am confused