मराठी

Find the maximum and minimum value, if any, of the following function given by g(x) = x3 + 1

Advertisements
Advertisements

प्रश्न

Find the maximum and minimum value, if any, of the following function given by g(x) = x3 + 1.

बेरीज
Advertisements

उत्तर

Here,  g(x) = x3 + 1.

g'(x) = 3x2 which is positive for x ∈ R.

g'(x) = 3x2 ≥ 0; ∀ x ∈ R

Hence g is an increasing function.

∴ It has no minimum and maximum value.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Application of Derivatives - Exercise 6.5 [पृष्ठ २३१]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 6 Application of Derivatives
Exercise 6.5 | Q 1.4 | पृष्ठ २३१

व्हिडिओ ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्‍न

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is π/3.


Find the maximum and minimum value, if any, of the following function given by f(x) = −(x − 1)2 + 10 


Find the maximum and minimum value, if any, of the following function given by h(x) = x + 1, x ∈ (−1, 1)


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 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:

`g(x) = x/2 + 2/x, x > 0`


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


Find the maximum value of 2x3 − 24x + 107 in the interval [1, 3]. Find the maximum value of the same function in [−3, −1].


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


Show that the right circular cone of least curved surface and given volume has an altitude equal to `sqrt2` time the radius of the base.


A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening


Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.


A given quantity of metal is to be cast into a half cylinder with a rectangular base and semicircular ends. Show that in order that the total surface area may be minimum the ratio of the length of the cylinder to the diameter of its semi-circular ends is \[\pi : (\pi + 2)\].


Show that a cylinder of a given volume, which is open at the top, has minimum total surface area when its height is equal to the radius of its base.


 A rod of 108 meters long is bent to form a rectangle. Find its dimensions if the area is maximum. Let x be the length and y be the breadth of the rectangle. 


A ball is thrown in the air. Its height at any time t is given by h = 3 + 14t – 5t2. Find the maximum height it can reach.


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.


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:

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.


Solve the following: 

Find the maximum and minimum values of the function f(x) = cos2x + sinx.


A rectangular sheet of paper has it area 24 sq. Meters. The margin at the top and the bottom are 75 cm each and the sides 50 cm each. What are the dimensions of the paper if the area of the printed space is maximum?


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


If f(x) = px5 + qx4 + 5x3 - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = ______.


The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is ______.


The sum of two non-zero numbers is 6. The minimum value of the sum of their reciprocals is ______.


A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs 300/- per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Re 1/- one subscriber will discontinue the service. Find what increase will bring maximum profit?


An open box with square base is to be made of a given quantity of cardboard of area c2. Show that the maximum volume of the box is `"c"^3/(6sqrt(3))` cubic units


If y = x3 + x2 + x + 1, then y ____________.


The function `"f"("x") = "x" + 4/"x"` has ____________.


The function `f(x) = x^3 - 6x^2 + 9x + 25` has


The maximum value of `[x(x - 1) + 1]^(2/3), 0 ≤ x ≤ 1` is


If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to ______.


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


The point in the interval [0, 2π], where f(x) = ex sin x has maximum slope, is ______.


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`


The absolute maximum value of the function f(x) = 2x3 − 3x2 − 36x + 9 defined on [−3, 3] is ______.


For a continuous function on a closed interval \[[a,b]\], which values must be compared to find absolute maxima and minima?


For \[f(x)=3x^4+4x^3-12x^2+12\], what is \[f'(x)\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×