Find the maximum and the minimum values, if any, without using derivatives of the following functions:

f(x) = 2x³ + 5 on R

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following functions. Also, find the points of inflection, if any:

#Mark the correct alternative in each of the following

The minimum value of is

Mark (√) against the correct answer in the following:

The minimum value of is

Mark (√) against the correct answer in the following:

The maximum value of is

Find the maximum or minimum values, if any, without using derivatives, of the function:

An isosceles triangle of vertical angle 2θ is inscribed in a circle of radius a. Show that the area of the triangle is maximum when .

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m³. If building of tank cost Rs 70 per square metre for the base and Rs 45 per square matre for sides, what is the cost of least expensive tank?

Divide 15 into two parts such that the square of one multiplied with the cube of the other is minimum.

Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible when revolved about one of its sides.

A closed cylinder has volume 2156 cm³. What will be the radius of its base so that its total surface area is minimum?