Consider the function f(x, y) = xª + y4 – x² – y? – 2xy. Find its stationary points. Show that one stationary point is a saddle point directly, and investigate the nature of the others using the second derivatives test.

Let g(x,y)=2xy with x=x(s, t)=s²+t² and y=y(s,t)=s/t. Calculate . gs and gt. Express your final answers as functions of s and t.

Consider the function:  f (x, y) = 2x2 + xy2 - 6xy + 5x + 2  1. Show that (1,3) is a stationary point of f. 2. Classify the stationary point (1,3).

Determine whether the functions y₁ and y₂ are linearly dependent on the interval (0,1). y₁ = tan ²t-sec c²t₁ y₂ = 6 Select the correct choice below and, if necessary, fill in the answer box within your choice. © A. Since y₁ = (y₂ on (0,1), the functions are linearly independent on (0,1). (Simplify your answer.) B. 1 Y₂ on (0,1), the functions are linearly dependent on (0,1). Since y₁ = (Simplify your answer.) C. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly independent on (0,1). D. Since y₁ is not a constant multiple of y₂ on (0,1), the functions are linearly dependent on (0,1).