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Shows that the triangle of greatest area...

Shows that the triangle of greatest area that can be inscribed in a circle is equilateral.

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Show that the rectangle of maximum area that can be inscribed in a given circle is a square.

Show that the radius of the right cicular cylinder of greatest curved surface that can be inscribed in a given cone is half the redius of the base of the cone.

An isosceles triangle of vertical angle 2 theta is inscribed in a circle of radius a. Show that the area of triangle is maximum when theta = (pi)/(6) .

Find the area of greatest rectangle that can be inscribed in an ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 .

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

SHARAM PUBLICATION-APPLICATIONS OF DERIVATIVES-EXAMPLE
  1. Show that the semi-vertical angle of the cone of the maximum volume an...

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  2. Show that the height of a closed right circular cylinder of given surf...

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  3. Shows that the triangle of greatest area that can be inscribed in a ci...

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  4. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  5. Find the minimum distance of a point on the curve 2/x^2+1/y^2= 1 from...

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  6. Find the minimum value of 64 sec theta + 27 cosec thetawhen theta lies...

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  7. Show that the minimum distance of a point on the curve (a^(2))/(x^(2))...

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  8. Show that the length of the portion of the tangent to x^(2/3) + y^(2/3...

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  9. Show that the sum of the intercepts on the coordinate axes of any tang...

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  10. Find the equation of the normal to the curve given by x = cos^3theta ,...

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  11. Find the point on the curve y^2-x^2 + 2x-1= 0 where the tangent is par...

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  12. Show that the tangent to the curve y=x^2+3x-2 at (1,2) is parallel to ...

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  13. Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan...

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  14. Find the altitude of a right circular cylinder of maximum volume inscr...

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  15. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

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  16. Find two numbers x and y whose sum is 15 such that xy^2 is maximum.

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  17. Find the values of x for which f(x) = x^4+2x^3-2x^2-6x+5 is locally ma...

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  18. Find the interval where y=sinx-cosx x in [0,2pi] is increasing.

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  19. Find the maximum value of y=(1+cosx) sinx,xepsilon[0,(3pi)/(4)]

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  20. Obtain the extreme point of f(x) = e^x (x^2-6x +9). As certain whether...

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