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Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

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Rectangles are inscribed inside a semi-circle of radius rdot Find the rectangle with maximum area.

Prove that , of all rectangles of given area , the square has the least perimeter.

If a triangle ABC inscribed in a fixed circle be slightly varies in such a way as to have its varies aways on the circle, then show that (da)/(cosA)+(db)/(cos B)+(dc)/(cos c)= 0

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be (a) sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

If a triangle ABC inscribed in a fixed circle be slightly varied in such a way that its vertices are always on the circle, show that, (da)/(cosA) + (db)/(cosB) + (dc)/(cosC)= 0 .

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NCERT BANGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum value of 2x^(3) – 24x + 107 in the interval [1, 3]. F...

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  2. It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attai...

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  3. Find the maximum and minimum values of x + sin 2x on [0, 2pi].

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  4. Find two numbers whose sum is 24 and whose product is as large as poss...

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  5. Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...

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  6. Find two positive numbers x and y such that their sum is 35 and the pr...

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  7. Find two positive numbers whose sum is 16 and the sum of whose cubes i...

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  8. A square piece of tin of side 18 cm is to be made into a box without t...

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  9. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wit...

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  10. Show that of all the rectangles inscribed in a given fixed circle, the...

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  11. Show that the right circular cylinder of given surface and maximum vol...

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  12. Of all the closed cylindrical cans (right circular), of a given volume...

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  13. A wire of length 28 m is to be cut into two pieces. One of the pieces ...

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  14. Prove that the volume of the largest cone that can be inscribed in a s...

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  15. Show that the right circular cone of least curved surface and given vo...

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  16. Show that the semi-vertical angle of the cone of the maximum volume an...

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  17. Show that semi-vertical angle of right circular cone of given surface ...

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  18. The point on the curve x^(2) = 2y which is nearest to the point (0, 5)...

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  19. For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2))...

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  20. The maximum value of [ x(x-1)+1]^((1)/(3)) , 0 lt= x lt= 1 is

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