हिंदी

Find the maximum and minimum value, if any, of the function given by f(x) = |x + 2| − 1. - Mathematics

Advertisements
Advertisements

प्रश्न

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

योग

उत्तर

Given function f(x) = |x + 2| - 1, f (x) ≥ -1; ∀ x ∈ R

|x + 2| has a minimum value of 0. 

∴ Minimum value of f = -1

x + 2 = 0 i.e., when x = -2

|x + 2| can have maximum value infinity.

Hence, the maximum value does not exist.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.5 [पृष्ठ २३२]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.5 | Q 2.1 | पृष्ठ २३२

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

Find the approximate value of cos (89°, 30'). [Given is: 1° = 0.0175°C]


Show that the height of the cylinder of maximum volume, that can be inscribed in a sphere of radius R is `(2R)/sqrt3.`  Also, find the maximum volume.


Find the maximum and minimum value, if any, of the following function given by f(x) = 9x2 + 12x + 2


Prove that the following function do not have maxima or minima:

g(x) = logx


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

`f(x) =x^3, x in [-2,2]`


Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3.`


 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. 


Find the maximum and minimum of the following functions : y = 5x3 + 2x2 – 3x.


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.


The profit function P(x) of a firm, selling x items per day is given by P(x) = (150 – x)x – 1625 . Find the number of items the firm should manufacture to get maximum profit. Find the maximum profit.


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.


By completing the following activity, examine the function f(x) = x3 – 9x2 + 24x for maxima and minima

Solution: f(x) = x3 – 9x2 + 24x

∴ f'(x) = `square`

∴ f''(x) = `square`

For extreme values, f'(x) = 0, we get

x = `square` or `square`

∴ f''`(square)` = – 6 < 0

∴ f(x) is maximum at x = 2.

∴ Maximum value = `square`

∴ f''`(square)` = 6 > 0

∴ f(x) is maximum at x = 4.

∴ Minimum value = `square`


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


If R is the circum radius of Δ ABC, then A(Δ ABC) = ______.


The maximum and minimum values for the function f(x) = 4x3 - 6x2 on [-1, 2] are ______


Find all the points of local maxima and local minima of the function f(x) = `- 3/4 x^4 - 8x^3 - 45/2 x^2 + 105`


Find the points of local maxima, local minima and the points of inflection of the function f(x) = x5 – 5x4 + 5x3 – 1. Also find the corresponding local maximum and local minimum values.


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. Also find the maximum volume.


AB is a diameter of a circle and C is any point on the circle. Show that the area of ∆ABC is maximum, when it is isosceles.


If x is real, the minimum value of x2 – 8x + 17 is ______.


The smallest value of the polynomial x3 – 18x2 + 96x in [0, 9] is ______.


Maximum slope of the curve y = –x3 + 3x2 + 9x – 27 is ______.


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


The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are ____________.


The distance of that point on y = x4 + 3x2 + 2x which is nearest to the line y = 2x - 1 is ____________.


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


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 ______.


If S1 and S2 are respectively the sets of local minimum and local maximum points of the function. f(x) = 9x4 + 12x3 – 36x2 + 25, x ∈ R, then ______.


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 ______.


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


Sum of two numbers is 5. If the sum of the cubes of these numbers is least, then find the sum of the squares of these numbers.


Find the maximum profit that a company can make, if the profit function is given by P(x) = 72 + 42x – x2, where x is the number of units and P is the profit in rupees.


Check whether the function f : R `rightarrow` R defined by f(x) = x3 + x, has any critical point/s or not ? If yes, then find the point/s.


A right circular cylinder is to be made so that the sum of the radius and height is 6 metres. Find the maximum volume of the cylinder.


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


Divide the number 100 into two parts so that the sum of their squares is minimum.


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×