English

F(X) = X3 \[-\] 1 on R . - Mathematics

Advertisements
Advertisements

Question

f(x) = x\[-\] 1 on R .

Sum
Advertisements

Solution

We can observe that f(x) increases when the values of x increase and f(x) decreases when the values of x decrease.

Also, f(x) can be reduced by giving smaller values of x.

Similarly, f(x) can be enlarged by giving larger values of x.

So, f(x) does not have a minimum or maximum value.

shaalaa.com
  Is there an error in this question or solution?
Chapter 18: Maxima and Minima - Exercise 18.1 [Page 7]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 18 Maxima and Minima
Exercise 18.1 | Q 9 | Page 7

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

f(x) = 4x2 + 4 on R .


f(x)=| x+2 | on R .


f(x)=sin 2x+5 on R .


f (x) = \[-\] | x + 1 | + 3 on R .


f(x) = x3  (x \[-\] 1).


f(x) =  (x \[-\] 1) (x+2)2


`f(x) = 2/x - 2/x^2,  x>0`


`f(x) = x/2+2/x, x>0 `.


f(x) = \[x^3 - 2a x^2 + a^2 x, a > 0, x \in R\] .


f(x) = \[x + \sqrt{1 - x}, x \leq 1\] .


The function y = a log x+bx2 + x has extreme values at x=1 and x=2. Find a and b ?


If f(x) = x3 + ax2 + bx + c has a maximum at x = \[-\] 1 and minimum at x = 3. Determine a, b and c ?


f(x) = (x \[-\] 2) \[\sqrt{x - 1} \text { in  }[1, 9]\] .


Find the absolute maximum and minimum values of the function of given by \[f(x) = \cos^2 x + \sin x, x \in [0, \pi]\] .


Find the absolute maximum and minimum values of a function f given by f(x) = 2x3 − 15x2 + 36x + 1 on the interval [1, 5].


A wire of length 20 m is to be cut into two pieces. One of the pieces will be bent into shape of a square and the other into shape of an equilateral triangle. Where the we should be cut so that the sum of the areas of the square and triangle is minimum?


Given the sum of the perimeters of a square and a circle, show that the sum of there areas is least when one side of the square is equal to diameter of the circle.


A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Find this maximum volume.


A large window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 metres find the dimensions of the rectangle will produce the largest area of the window.


An isosceles triangle of vertical angle 2 \[\theta\] is inscribed in a circle of radius a. Show that the area of the triangle is maximum when \[\theta\] = \[\frac{\pi}{6}\] .


Show that among all positive numbers x and y with x2 + y2 =r2, the sum x+y is largest when x=y=r \[\sqrt{2}\] .


Find the maximum slope of the curve y = \[- x^3 + 3 x^2 + 2x - 27 .\]


An open tank is to be constructed with a square base and vertical sides so as to contain a given quantity of water. Show that the expenses of lining with lead with be least, if depth is made half of width.


A box of constant volume c is to be twice as long as it is wide. The material on the top and four sides cost three times as much per square metre as that in the bottom. What are the most economic dimensions?


The space s described in time by a particle moving in a straight line is given by S = \[t5 - 40 t^3 + 30 t^2 + 80t - 250 .\] Find the minimum value of acceleration.


Write sufficient conditions for a point x = c to be a point of local maximum.


The maximum value of x1/x, x > 0 is __________ .


The number which exceeds its square by the greatest possible quantity is _________________ .


The least value of the function f(x) = \[x3 - 18x2 + 96x\] in the interval [0,9] is _____________ .


The least and greatest values of f(x) = x3\[-\] 6x2+9x in [0,6], are ___________ .


If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is ______________ .


If(x) = \[\frac{1}{4x^2 + 2x + 1}\] then its maximum value is _________________ .


Let x, y be two variables and x>0, xy=1, then minimum value of x+y is _______________ .


A wire of length 34 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a rectangle whose length is twice its breadth. What should be the lengths of the two pieces, so that the combined area of the square and the rectangle is minimum?


The minimum value of the function `f(x)=2x^3-21x^2+36x-20` is ______________ .


Which of the following graph represents the extreme value:-


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×