1. Find and evaluate the maxima, minima and saddle points of the function =xy(x^{2}+y^{2}-1) "f(x,y)=xy(x^{2}+y^{2}-1)")
2. Show that=x^{3}-12xy+48x+by^{2},b\neq0 "f(x,y)=x^{3}-12xy+48x+by^{2},b\neq0")
has two, one or zero stationary points according to whether |b| is less than,equal to or greater than 3.
3. Locate the stationary points of the function
=(x^{2}-y^{2})exp[-(x^{2}+y^{2})/a^{2}] "f(x,y)=(x^{2}-y^{2})exp[-(x^{2}+y^{2})/a^{2}]")
4. Find the stationary points of the function=x^{3}+xy^{2}-12x-y^{2} "f(x,y)=x^{3}+xy^{2}-12x-y^{2}")
and identify their natures
5. Find the stationary values of=4x^{2}+4y^{2}+x^{4}-6x^{2}y^{2}+y^{4} "f(x,y)=4x^{2}+4y^{2}+x^{4}-6x^{2}y^{2}+y^{4}")
and classify them as maxima, minima or saddle points.
6. The temperature of the point (x,y,z) on the unit sphere is given by T(x,y,z)=1+xy+yz.
By using the method of Lagrange multipliers find the temperature of the hottest point on the sphere.
Stationary points set 1 http://ellipticalkoyal.blogspot.com/2019/01/stationary-points-of-two-variable.html2. Show that
has two, one or zero stationary points according to whether |b| is less than,equal to or greater than 3.
3. Locate the stationary points of the function
4. Find the stationary points of the function
5. Find the stationary values of
6. The temperature of the point (x,y,z) on the unit sphere is given by T(x,y,z)=1+xy+yz.
By using the method of Lagrange multipliers find the temperature of the hottest point on the sphere.
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