Show that among all positive numbers x and y with x2 + y2 = r2, the sum x + y is largest when x = y = .

x,y are positive numbersx2 + y2 = r2 is the given conditionTherefore,LetAnd,

Q28 of 137 Page 19

Show that among all positive numbers x and y with x² + y² = r², the sum x + y is largest when x = y = .

x,y are positive numbers

x² + y² = r² is the given condition

Therefore,

Let

And,

A closed cylinder has volume 2156 cm³. What will be the radius of its base so that its total surface area is minimum?

Show what the maximum volume of the cylinder which can be inscribed in a sphere of radius cm is 500 π cm³ .

Determine the points on the curve x² = 4y which are nearest to the point (0, 5).

Find the point on the curve y² = 4x which is nearest to the point (2, –8).