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Show that the semivertical angle of a co...

Show that the semivertical angle of a cone of maximum volume and of given slant height is `tan^(-1)sqrt2`

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Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1) sqrt(2) .

Show that the semivertical angle of a cone of given slant height and maximum volume is tan^(-1)sqrt(2) .

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is sin^(-1) ((1)/(3)) .

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm .

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3))

The total surface area of a right circular cone is given . Show that the volume of the cone is maximum when the semi-vertical angle is sin^(-1)(1/3) .

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt(2) time the radius of the base.

The total surface area of a right circular cone is given. Show that the volume of that cone will be maximum if the semivertical angle is sin^(-1)1/3 .

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
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  2. In a right -angled triangle, prove that r+2R=S.

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  3. Show that the semivertical angle of a cone of maximum volume and of gi...

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  4. Let f(x)={(|x-2|+a^2-9a-9,ifxlt2, 2x-3 ,ifxge2:} Then find value of 'a...

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  5. Find the values of 'm' for which the equation x^4-(m-3)x^2+m=0 has Fo...

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  6. The difference between the greatest and least values of the function f...

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  7. The tangent and normal to the curve y=2sinx+sin2x are drown at P(x=pi/...

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  8. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

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  9. Find the point on the curve y-e^(xy)+x=0. At which we have vertical ta...

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  10. Find the lengths of tangent, subtangent, normal and subnormal to y^2=4...

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  11. If the length of subnormal is equal to length of subtangent at a point...

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  12. Find the angle of intersection between the following curves, y^2=4x an...

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  13. Show that x=y^2 and xy = k cut orthogonally if 8k^2=1

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  14. Show that curves ax^2+by^2=1 and cx^2+dy^2=1 intersect orthogonally if...

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  15. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

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  16. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  17. Verify Rolle's theorem for f(x)=x^3(x-1)^2 in the interval 0lexle1

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  18. If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

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  19. The value of 'c' of Rolls's throrem is applicable to the function f(x)...

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  20. Find 'c' of the Lagrange's mean value theorem for the function f(x)=3x...

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