CBSE Class 12-science Maths Applications of Derivatives
- Fimd the point of local maxima and local minima and corresponding local maxima and local minima values of each of the following funct. F(x) = x^3 -2ax^2 a^2x, a>0 ,x belongs to real no.
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- Show that the volume of largest cone that can be inscribed in a sphere of radius R is of the volume of the sphere.
- Show that the rectangle of maximum area that can be inscribed in a circle of radius r is a square of side
- A square piece of tin of side 18 cm is to made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum. On four sides of this box, write four life skills.
- Suppose a company manufactures x units. And the cost of manufacturing these x units comes out to be a cost function given as c(x)=2x3 -60x2 +1500. Definitely the company would like to minimise its cost to attain maximum profit. So here we would like to know how many units should be manufactured to get minimum cost,
- Suppose a certain sheet of metal is given and we need to make a right circular cylinder tin out of it such that it contains maximum quantity of oil. Here we assume no metal is wasted.
- A window is in the form of a rectangle surmounted by a semi circular opening. The total perimeter of the window is 10 m. Find the dimensions o the window to admit maximum light through the whole opening. Do you think that by getting maximum light, we can save electricity? Do you agree that we should save electricity?
- Show that the height of cylinder of maximum volume that can be inscribed in a sphere of radius R is Also find maximum volume.
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