Using the chain rule, find the min and max points and their values of the composite function defined by:

Question

z= x^2 + y^2, x=sin(2t), y=cos(t)

Answer 1

z = x^2 + y^2
dz/dt = 2x dx/dt + 2y dy/dt
= 2sin(2t) * 2cos(2t) + 2cos(t) * (-sin(t))
= 4cos(4t) - sin(2t)

for dz/dt=0, check wolframalpha and enter

solve 4cos(4t) - sin(2t) = 0

Answer 2

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