Which test can be used to determine whether a critical point (a, b) is a local minimum, local maximum, or a saddle point for a function f(x,y)𝑓(𝑥,𝑦)?a.First Partial Derivative Testb.Critical Point Testc.Second Partial Derivative Testd.Lagrange Multiplier Test

Use the first derivative test to find the two critical points of the function. First point:(Either of the points can be 𝑥1 or 𝑥2.)𝑥1= Relative Maximum Relative Minimum Neither

Use the first derivative test to find the two critical points of the function. First point:

For the function of two variables, f (x, y) = x3 − y2 + 9xy + 5. Find the critical points and determine their nature to complete the following sentences (making sure you use at least 3 decimal places in your answer): • the left-most stationary point (the one with the lower value of x) is located at x = and y = and is a point. • the right-most stationary point (the one with the higher value of x) is located at x = and y = and is a point

Consider the function and fill in the spaces below.  By the First derivative test, the function has:a local maximum at the point Answer 1 Question 7, Answer 2 Question 7 and a local minimum at the point

[5 marks] Locate all relative maxima, relative minima and saddle points of thefunction f (x, y) = xy − x3 − y2.