Q3) Critical Points of a function (3 marks) i) Generate a third degree polynomial in x and y named g(x,y) that is based

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Q3) Critical Points of a function (3 marks)
i) Generate a third degree polynomial in x and y named g(x,y)
that is based on your mobile number (Note : In case there is a 0 in
one of the digits replace it by 3). Suppose your mobile number is
9412821233, then the polynomial would be g(x,y) = 9x3 −4x2y+ 1xy2
−2y3 + 8x2 −2xy+ y2 −2x + 3y −3, where alternate positive and
negative sign are used.
Deliverable(s) : The polynomial constructed should be reported.
(0.5)
ii) Write a code in Python to find all critical points of
g(x,y). You may use built in functions like ’solve’ (or other
similar functions) in Octave/Matlab to find the critical points
.
Deliverable(s) : The code that finds the critical points along
with the display of all the calculated critical points. (1)
iii) Write a code in Python to determine whether they correspond
to a maximum, minimum or a saddle point.
Deliverable(s) : The code that identifies the type of critical
points. The critical points and their type must be presented in the
form of the table generated by code for the above polynomial. (1.5
marks)