Sketch the level curve of the function z(x, y) = y² — x² for c = 16. - 10- 9 8 7 6 5 4 3 2 + -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 -7 -8 -9 10- 1 2 3 4 5 6 7 8 9 10

Sketch the graph of a differentiable function y = ƒ(x) that has a local minimum at (1, 1) and a local maximum at (3, 3);

Find the critical points of the function f (x, y) = - x2+ 4xy+ xy2 and determine whether the critical points are local maximum, local minimum or saddle.

Find the critical points for the function: f(x,y)=x3+y3-9x2-48y-3 and use the Second Derivative Test to classify each as a local maximum, local minimum, saddle point, or none of these.

use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to two decimal places.

what is the largest vertical distance between the graphs of the functions y=x^1/2 and y=x^2 in the interval [0,1].

Find the critical numbers of the function.                                                             g(x) = x − √x

The number of defects on the front side (X) of a wooden panel and the number of defects  on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3.Determine the marginal pmf of X. Determine the conditional pmf of Y given X=2.

Draw a contour map of the function showing several level curves. f(x, y) = xy