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1. In questions 1.1 to 1.7 below, one or more of the alternatives are correct.  Write the code letter(s) a, b, c, d corresponding to the correct alternative(s) in the answer book.  Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is picked up.

1.7 The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has

1. no local extremum
2. one local minimum but no local maximum
3. one local maximum but no local minimum
4. one local minimum and one local maximum

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r = $\frac{\partial^2 f}{\partial x^2}$ = 2y

s = $\frac{\partial^2 f}{\partial x \partial y}$ = 2x - 3

t = $\frac{\partial^2 f}{\partial y^2}$ = 0

Since, rt - s2 <= 0, (if < 0 then we have no maxima or minima, if = 0 then we can't say anything).

Maxima will exist when rt - s2 > 0 and r < 0.

Minima will exist when rt - s2 > 0 and r > 0.

Since, rt - s2 is never > 0 so we have no local extremum.

answered by Boss (34.2k points)
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When x = 1.5, s2 = 0 and 0 - 0 = 0.

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Corrected.