Could you help me understand this better? Thank you!

Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) f ( x, y) = x3 + y3 - 3x2 - 6y2 - 9x local maximum value(s) X local minimum value(s) X saddle point(s) ( x, y ) = XFind and classify the critical points of f (x, y) - r - 3x- - 92 + y" - 6y-. SOLUTION The first step is to find all the first-order partial derivatives: (x) - 3x3 - 9x + y) - 6y?) - 3 (x -3) (x + 1) (for steps, see partial derivative calculator). - (2) - 3x7 - 9x + y' - 6y') - 3y (y - 4) (for steps, see partial derivative calculator). 0 (3 (x-3) (x+1) -0 Next, solve the system . or By (y - 4) - 0 The system has the following real solutions: (, y) - (-1, 0). (x, y) - (-1. 4). (x, y) - (3, 0). (r, y) - (3, 4). Now, let's try to classify them. Find all the second-order partial derivatives: # (x] -3x3 - 9x + y) - 6y?) - 6x - 6 ( for steps, see partial derivative calculator). (pil - 3x' -9x + y' - 6y ) - 0 ( for steps, see partial derivative calculator). # (x3 - 3x3 - 9x + y' - 6y') - by - 12 (for steps, see partial derivative calculator) Define the expression D - Of - 36 (x - 1) (y - 2). Since D (-1, 0)) - 144 is greater than ( and (x) - 323 -92 + y' - by') |((x,y)-(-1.0)) - -12 is less than 0), it can be stated that (-1, 0) is a relative maximum. Since D(-1, 4) - -144 is less than (), it can be stated that (-1, 4) is a saddle point Since D(3, 0) - -144 is less than 0, it can be stated that (3, () is a saddle point. Since D (3, 4) - 144 is greater than () and (21 - 323 - 9x + y' - 6y") |(my)_(34)) - 12 is greater than 0, it can be stated that (3, 4) is a relative minimum. ANSWER Relative Maxima (x, y) - (-1,0) a, f (-1, 0) - 5A Relative Minima (c, y) - (3, 4) A, f(3, 4) - -59 A Saddle Points (x, y) - (-1, 4) A, f (-1, 4) - -27 A (x, y) - (3, 0) A, f(3, 0) - -27 Af (x, y) = x3+y3 - 3x2 - 6y - Input... 1 ru -8 6 -2 1 11 -B -21 41