## anonymous 4 years ago Find the maximum and minimum values of f(x,y)=xy on the ellipse 6x2+y2=5. Please help!!

first solve ellipse equation for y $y = \sqrt{5-6x^{2}}$ substitute into f(x,y) $f(x) = x \sqrt{5-6x^{2}}$ set derivative equal to 0 to find min/max $f'(x) = \sqrt{5-6x^{2}}-\frac{6x^{2}}{\sqrt{5-6x^{2}}} = \frac{5-12x^{2}}{\sqrt{5-6x^{2}}}$ f'(x) = 0 when numerator is 0 $5-12x^{2} = 0$ $\ x = \pm \sqrt{\frac{5}{12}} \approx \pm 0.6455$ $\max \rightarrow f(.6455) \approx 1.02$ $\min \rightarrow f(-.6455) \approx -1.02$