5778

Mathematics Integration Level: Misc Level

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


5777

Mathematics Integration Level: Misc Level

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


5776

Mathematics Integration Level: Misc Level

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


5775

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


5774

Mathematics Integration Level: Misc Level

Find two positive numbers x and y such that their sum is 35 and the product x2y5 is maximum


5773

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


5772

Mathematics Integration Level: Misc Level

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


5752

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<\frac{\pi}{2}


5751

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)=\frac{1}{x^{2}+2}


5750

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)=\frac{x}{2}+\frac{2}{x}, x>0


5749

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) = 2x3 -6x2 + 6x + 5


5747

Mathematics Integration Level: Misc Level

Find the turning points of function f(x) = 4x3 + 19x2 - 14x + 3 amd distinguish between them. Also find the local maximum and the minimum values of the function.


5745

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]


5742

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,\pi]


5741

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)=\left ( \frac{1}{2}-x \right )^{2}+x^{3} in [-2,2.5]


Displaying 16-30 of 195 results.