Find the critical points of the given function and then determine whether they are local maxima, local minima, or saddle points.
f(x, y) = cos(x2 + y2) consider only the three critical points (0, 0), π 2 , π 2 , and (0, π )
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Answer:
Step-by-step explanation:
The vertex of this parabola is the midpoint of the focus (-2,4) and where the directrix intersects the axis of symmetry of the parabola (-2,6)
This parabola must open downwards due to the position of the directrix and has equation of the form:
where (h,k) is the vertex.
This implies that:
and
The value of p is the distance from the vertex to the focus:
We substitute all the values into the formula to get:
Or