Maxima and minima class 12 | Second derivative test | application of derivatives class 12
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 2R/√3. A rectangle is inscribed in a semi-circle of radius r with one of its sides on diameter of semi-circle. Find the dimensions of the rectangle so that its area is maximum. Find also the area. Prove that a conical tent of given capacity will require the least amount of canvas when the height is √2 times the radius of the base. 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. Prove that the semi vertical angle of the right circular cone of given volume and least curved surface is cot-1(√2). An isosceles triangle of vertical angle 2theta is inscribed in a circle of radius a. Show that the area of the triangle is maximum when theta = π/6. Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6√3r. Find the dimensions of the rectangle of perimeter 36cm which will sweep out a volume as large as possible when revolved about one of its sides. Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12cm is 16cm. A closed cylinder has volume 2156cm³. What will be the radius of its base so that its total surface area is minimum? Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius 5√3 cm is 500π cm³. @Amit Ranjan Mathematics Maxima and minima class 12 | Second derivative test | application of derivatives class 12 - differentiation Links of class 12 maths playlist Chapter 23 to Chapter 27 Algebra of vectors | dot product | cross product | scalar triple product | direction cosines and direction ratios • algebra of vectors class 12 | scalar or do... Chapter 22 DIFFERENTIAL EQUATIONS • differential equations class 12 Chapter 9 and 10 Continuity and diffrentiability • continuity and differentiability class 12 Chapter 4 INVERSE TRIGNOMETRIC FUNCTIONS • inverse trigonometric functions class 12 Chapter 1 ,2 Relation And Function • relation and function class 12 Chapter 28 Straight Line In Space • Straight line in space class 12 Chapter 29 The Plane • the plane class 12 Chapter 11 Differentiation • differentiation class 12 Mathematics | rd ... Chapter 19 Indefinite Integral • ….. Chapter 20 Definite Integration • definite integration class 12 Chapter 5,6,7 and 8 algebra of matrices , determinant , adjoint and inverse of matrix and simultaneous linear equation • Matrix and determinants (2022-23) Chapter 14 to chapter 18 Application Of Derivative • Application Of Derivatives For Class 12 - ... Chapter 30 to chapter 32 probability , random variables and binomial distribution • probability class 12 | rd sharma 2022-23 #maximaminima #applicationofderivativesclass12 #differentiation #derivatives #calculus
