Please show your work 1) Use implicit differentiation to find dz/dx and dz/dy. a
ID: 3289170 • Letter: P
Question
Please show your work
1) Use implicit differentiation to find dz/dx and dz/dy. assume that equation defines z as a differentiable function near each (x,y)
Ln(x^2+y^2)-z=tan^1(x+z)
2) Given that r=(x^2+y^2)^1/2 show that dr/dx= x/(x^2+y^2)^1/2 = x/r =cos theta. starting from r=x/cos theta , does it follow that dr/dx = 1/ cos theta? Explain why its not possible for both calculations to be correct
3)locate all critical points and classify them using the second derivative test
a) 2x^2+y^3-x^2y-3y
b) f(x,y)= xsiny
4) Use Lagrange multipliers to find the closest point on the given curve to the indicated point.
y=x^2,(3,0)
Explanation / Answer
3)b)df/dx=siny
df/dy=xcosy, so critical points (a,npi),(0,b), (b,npi/2) n odd