English

The function f(x) = x log x is minimum at x = ______.

Advertisements
Advertisements

Question

The function f(x) = x log x is minimum at x = ______.

Options

  • e

  • `1/e`

  • 1

  • `-1/e`

MCQ
Fill in the Blanks
Advertisements

Solution

The function f(x) = x log x is minimum at x = `underlinebb(1/e)`.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.2: Applications of Derivatives - MCQ

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

An open box is to be made out of a piece of a square card board of sides 18 cms by cutting off equal squares from the comers and turning up the sides. Find the maximum volume of the box.


Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`h(x) = sinx + cosx, 0 < x < pi/2`


Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

f (x) = sin x + cos x , x ∈ [0, π]


Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x2.


Find two positive numbers x and y such that x + y = 60 and xy3 is maximum.


Show that the right circular cylinder of given surface and maximum volume is such that is heights is equal to the diameter of the base.


A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?


Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is `8/27` of the volume of the sphere.


The point on the curve x2 = 2y which is nearest to the point (0, 5) is ______.


The maximum value of `[x(x −1) +1]^(1/3)` , 0 ≤ x ≤ 1 is ______.


Find the absolute maximum and minimum values of the function f given by f (x) = cos2 x + sin x, x ∈ [0, π].


A metal box with a square base and vertical sides is to contain 1024 cm3. The material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box


Find the maximum and minimum of the following functions : f(x) = `x^2 + (16)/x^2`


Find the maximum and minimum of the following functions : f(x) = x log x


Find the maximum and minimum of the following functions : f(x) = `logx/x`


Divide the number 30 into two parts such that their product is maximum.


Divide the number 20 into two parts such that sum of their squares is minimum.


An open cylindrical tank whose base is a circle is to be constructed of metal sheet so as to contain a volume of `pia^3`cu cm of water. Find the dimensions so that the quantity of the metal sheet required is minimum.


Show that the height of a closed right circular cylinder of given volume and least surface area is equal to its diameter.


Find the volume of the largest cylinder that can be inscribed in a sphere of radius ‘r’ cm.


Solve the following : Show that a closed right circular cylinder of given surface area has maximum volume if its height equals the diameter of its base.


Solve the following : Show that the height of a right circular cylinder of greatest volume that can be inscribed in a right circular cone is one-third of that of the cone.


Solve the following:

A rectangular sheet of paper of fixed perimeter with the sides having their lengths in the ratio 8 : 15 converted into an open rectangular box by folding after removing the squares of equal area from all corners. If the total area of the removed squares is 100, the resulting box has maximum volume. Find the lengths of the rectangular sheet of paper.


Divide the number 20 into two parts such that their product is maximum.


Examine the function for maxima and minima f(x) = x3 - 9x2 + 24x


A rod of 108 m long is bent to form a rectangle. Find it’s dimensions when it’s area is maximum.


The minimum value of Z = 5x + 8y subject to x + y ≥ 5, 0 ≤ x ≤ 4, y ≥ 2, x ≥ 0, y ≥ 0 is ____________.


If z = ax + by; a, b > 0 subject to x ≤ 2, y ≤ 2, x + y ≥ 3, x ≥ 0, y ≥ 0 has minimum value at (2, 1) only, then ______.


A metal box with a square base and vertical sides is to contain 1024 cm3. The material for the top and bottom costs Rs 5/cm2 and the material for the sides costs Rs 2.50/cm2. Find the least cost of the box.


The maximum value of sin x . cos x is ______.


Find the points of local maxima and local minima respectively for the function f(x) = sin 2x - x, where `-pi/2 le "x" le pi/2`


The function f(x) = x5 - 5x4 + 5x3 - 1 has ____________.


Let f(x) = 1 + 2x2 + 22x4 + …… + 210x20. Then f (x) has ____________.


Let x and y be real numbers satisfying the equation x2 – 4x + y2 + 3 = 0. If the maximum and minimum values of x2 + y2 are a and b respectively. Then the numerical value of a – b is ______.


Let f(x) = (x – a)ng(x) , where g(n)(a) ≠ 0; n = 0, 1, 2, 3.... then ______.


The greatest value of the function f(x) = `tan^-1x - 1/2logx` in `[1/sqrt(3), sqrt(3)]` is ______.


The minimum value of 2sinx + 2cosx is ______.


A rod AB of length 16 cm. rests between the wall AD and a smooth peg, 1 cm from the wall and makes an angle θ with the horizontal. The value of θ for which the height of G, the midpoint of the rod above the peg is minimum, is ______.


A straight line is drawn through the point P(3, 4) meeting the positive direction of coordinate axes at the points A and B. If O is the origin, then minimum area of ΔOAB is equal to ______.


If f(x) = `1/(4x^2 + 2x + 1); x ∈ R`, then find the maximum value of f(x).


A metal wire of 36 cm long is bent to form a rectangle. Find its dimensions when its area is maximum.


If x + y = 8, then the maximum value of x2y is ______.


A box with a square base is to have an open top. The surface area of box is 147 sq. cm. What should be its dimensions in order that the volume is largest?


Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) `= x sqrt(1 - x), 0 < x < 1`


Mrs. Roy designs a window in her son’s study room so that the room gets maximum sunlight. She designs the window in the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the window that will admit maximum sunlight into the room.


20 is divided into two parts so that the product of the cube of one part and the square of the other part is maximum, then these two parts are


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×