Q.3 (a) Discuss the maxima and minima of (x²+y²+8x+6y+6) .

f=x²+y²+8x+6y+6 . Stationary points: f_x=2x+8=0⇒ x=-4 ; f_y=2y+6=0⇒ y=-3 . Stationary point (-4,-3) . Second derivatives: r=f_xx=2,\ s=f_xy=0,\ t=f_yy=2 . rt-s²=4>0 and r>0 . So f has a minimum at (-4,-3) : f_min=16+9-32-18+6=-19 . There is no maximum.

Discuss the maxima and minima of \((x^2+y^2+8x+6y+6)\).

Q.3 (a) Discuss the maxima and minima of \((x^2+y^2+8x+6y+6)\).

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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\(f=x^2+y^2+8x+6y+6\).

Stationary points: \(f_x=2x+8=0\Rightarrow x=-4\); \(f_y=2y+6=0\Rightarrow y=-3\). Stationary point \((-4,-3)\).

Second derivatives: \(r=f_{xx}=2,\ s=f_{xy}=0,\ t=f_{yy}=2\). \(rt-s^2=4>0\) and \(r>0\).

So f has a minimum at \((-4,-3)\): \(f_{min}=16+9-32-18+6=\mathbf{-19}\). There is no maximum.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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Discuss the maxima and minima of \((x^2+y^2+8x+6y+6)\).

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