i had a worksheet on applications of derivatives with 63 questions and i couldnt solve 12 of them, it would be great if you could help me.

1) The volume of a cube is increasing at a constant rate. prove that the increase in surface area varies inverslyas the length of the edge of the cube.
2) An open topped box is to be constructed by removing equal squares from each corner of a 3m X 8m ractangularsheet of aluminium and folding up the sides. Find the volume of the largest such box.
3) Prove that the area of the right angled triangle, of given hypotenuse, is maximum when triangle is isosceles.
4) A closed cylinder has volume 2156cm^3. what will be the radius of the base so that it's total surface area is minimum.
5) Two sides of a triangle have lengths 'a' and 'b' and the angle between them is 'theta'. what value of 'theta' will maximize the area of the triangle? Find the maximum area of the triangle also.
6) Find the shortest distance of the point (0,c) from the parabola y=x^2, 0 < = c < = 5.
7) Find a point on the curve y =(x-3)^2, where the tangent is parallel to the line joining (4,1) and (3,0).
8) Discuss the applicability of Rolle's Theormfor the function f(x)= cos 1/x, on [-1,1].
9) Show that f(x) = (x-1)e^x + 1 is a strictly increasing function for all x > 0.
10) If the length of 3 sides of a trapezium other tan base is equal to 10cm, then find the area of the trapezium when it is maximum.
11) Find the intervals in which the function f(x) = x^4 - 8x^3 + 22x^2 - 24x+21 is increasing or decreasing.
12) Find the point on the curve y^2 = 4x which is nearest to the point (2,1).

Thanks :)