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Find both the maximum value and the minimum value of 3x4 − 8x3 + 12x2 − 48x + 25 on the interval [0, 3].
Concept: undefined >> undefined
At what points in the interval [0, 2π], does the function sin 2x attain its maximum value?
Concept: undefined >> undefined
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What is the maximum value of the function sin x + cos x?
Concept: undefined >> undefined
Find the maximum value of 2x3 − 24x + 107 in the interval [1, 3]. Find the maximum value of the same function in [−3, −1].
Concept: undefined >> undefined
It is given that at x = 1, the function x4− 62x2 + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.
Concept: undefined >> undefined
Find the maximum and minimum values of x + sin 2x on [0, 2π].
Concept: undefined >> undefined
Find two numbers whose sum is 24 and whose product is as large as possible.
Concept: undefined >> undefined
Find two positive numbers x and y such that x + y = 60 and xy3 is maximum.
Concept: undefined >> undefined
Find two positive numbers x and y such that their sum is 35 and the product x2y5 is a maximum.
Concept: undefined >> undefined
Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
Concept: undefined >> undefined
A square piece of tin of side 18 cm is to made into a box without a top by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
Concept: undefined >> undefined
A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square 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 the maximum possible?
Concept: undefined >> undefined
Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
Concept: undefined >> undefined
Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?
Concept: undefined >> undefined
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 length of the two pieces so that the combined area of the square and the circle is minimum?
Concept: undefined >> undefined
Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is `8/27` of the volume of the sphere.
Concept: undefined >> undefined
Show that the right circular cone of least curved surface and given volume has an altitude equal to `sqrt2` time the radius of the base.
Concept: undefined >> undefined
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is `tan^(-1) sqrt(2)`
Concept: undefined >> undefined
Show that semi-vertical angle of right circular cone of given surface area and maximum volume is `Sin^(-1) (1/3).`
Concept: undefined >> undefined
The point on the curve x2 = 2y which is nearest to the point (0, 5) is ______.
Concept: undefined >> undefined
