Please help for my test CALculus
posted by Lucy on .
using the chain rule find the min and max points and their values of the composite function defined by z=x^2+y^2, x=sin(2t), y=cos(t)
This is what Ive got so far...
I understand the steps of computing the max and min I just can't seem to solve this problem. Its on a test I have due tomorrow so please help!!
You need to find dz/dt=0, so set
Expand using double-angle formulae:
8cos(t)sin(t)(cos(t)^2-sin(t)^2)-2cos(t)sin(t) = 0
t=0, t=π/2, t=π and t=3π/2
when sin(t)=0 or cos(t)=0.
This leaves us with:
which can be reduced by the substitution
to a quadratic equation equivalent to
Now that leaves you to check each point as a maximum/minimum or inflection point using second derivatives.
vai toma no cu
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