If xy = 10, Then Minimum Value Of 12x2 + 13y2 is Equal To

A box of constant volume C is to be twice as long as it is wide. The cost per unit area of the material on the top and four sides is three times the cost for bottom. What are the most economical dimensions of the box?  

Find the maximum surface area of a cylinder that can be inscribed in a given sphere of radius R.  

Find the semi-vertical angle of the cone of maximum curved surface area that can be inscribed in a given sphere of radius R.

Find the point on the curve y = x² which is closest to the point A(0, a).  

Find the shortest distance between the line y – x = 1 and the curve x = y².

Find the vertical angle of right circular some of minimum curved surface that circumscribes in a given sphere.

 A, B > 0, then minimum value of sec A + sec B is equal to   

f (x) = x² – 4 | x | and

Then f (x) has    

The function f (x) = x (x² – 4)ⁿ (x² – x + 1), n Ïµ N assumes a local minima at x = 2, then