Mathematics Integration Level: Misc Level

Two sides of at triangle have lengths a and b, and the angle between them is . What value of will maximize the area of triangle? Also find the maximum area of the triangle

Mathematics Integration Level: Misc Level

Prove that of all rectangles with given perimeter, the square has the largest area

Mathematics Integration Level: Misc Level

Prove that the perimeter of a right-angled triangle of given hypotenuse is maximum when the triangle is isosceles

Mathematics Integration Level: Misc Level

Three numbers are given whose sum is 180 and the ratio of first two of them is 1:2 if the product of the numbers is greatest, find the numbers

Mathematics Integration Level: Misc Level

Find two positive numbers x and y such that their sum is 35 and the product x^{2}y^{5} is maximum

Mathematics Integration Level: Misc Level

The sum of two positive numbers is 20. Find the numbers if the product of the squares of one and the cube of the other is maixmum

Mathematics Integration Level: Misc Level

The sum of two positive numbers is 20. Find the numbers if the sum of their squares is minimum

Mathematics Integration Level: Misc Level

Find the points of local maxima and minima (if any) of the following function. Also find the local maxima and minima values

f(x) = Sin x + Cos x, 0<x<

Mathematics Integration Level: Misc Level

Find the points of local maxima and minima (if any) of the following function. Also find the local maxima and minima values

Mathematics Integration Level: Misc Level

Find the points of local maxima and minima (if any) of the following function. Also find the local maxima and minima values

Mathematics Integration Level: Misc Level

f(x) = 2x^{3} -6x^{2} + 6x + 5

Mathematics Integration Level: Misc Level

Find the turning points of function f(x) = 4x^{3} + 19x^{2} - 14x + 3 amd distinguish between them. Also find the local maximum and the minimum values of the function.

Mathematics Integration Level: Misc Level

Find the (absolute) maximum and the (absolute) minimum values of the following function in the indicated intervals. Also find the points of (absolute) maxima and minima

f(x) = 3 + |x+1| in [-2,3]

Mathematics Integration Level: Misc Level

Find the (absolute) maximum and the (absolute) minimum values of the following function in the indicated intervals. Also find the points of (absolute) maxima and minima

f(x) = Sin x + Cos x in [0,]

Mathematics Integration Level: Misc Level

Find the (absolute) maximum and the (absolute) minimum values of the following function in the indicated intervals. Also find the points of (absolute) maxima and minima