MAXIMA AND MINIMA

MAXIMA AND MINIMA

​P-1

Find the largest possible area of a right-angled triangle whose hypotenuse is 5 cm long.

MAXIMA AND MINIMA

​P-2

Two sides of a triangle have lengths a and band the angle between them is θ. What value of θ will maximize the area of the triangle? Find the maximum area of the triangle also.  

MAXIMA AND MINIMA

​P-3

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?

MAXIMA AND MINIMA

​P-4

Given the sum of the perimeters of a square and a circle, show that the sum of there areas is least when one side of the square is equal to diameter of the circle.

MAXIMA AND MINIMA

​P-5

A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Find this maximum volume.

MAXIMA AND MINIMA

​P-6

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without a top, by cutting off squares from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum possible?

Multiple Choice

Divide 15 into two parts such that the square of one multiplied by the cube of the other is minimum.

• 5 and 10

• 6 and 9

• 12 and 3

• none of these

MAXIMA AND MINIMA

​P-7

A window in the form of a rectangle is surmounted by a semi-circular opening. The total perimeter of the window is 10 m. Find the dimension of the rectangular of the window to admit maximum light through the whole opening.

MAXIMA AND MINIMA

​P-8

A window in the form of a rectangle is surmounted by a semi-circular opening. The total perimeter of the window is 10 m. Find the dimension of the rectangular of the window to admit maximum light through the whole opening.

MAXIMA AND MINIMA

​P-9

Find the maximum slope of the curve y = - x³+ 3x² + 9x − 27

MAXIMA AND MINIMA

​P-10

Show that of all the rectangles of a given area, the square has the smallest perimeter.

MAXIMA AND MINIMA

​P-11

Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube.