Advertisements
Advertisements
Question
f(x)=| x+2 | on R .
Solution
Given: f(x) = \[\left| x + 2 \right|\]
Now,
\[\left| x + 2 \right| \geq 0\] for all x \[\in\] R
Thus, f(x) \[\geq\] 0 for all x \[\in\] R
Therefore, the minimum value of f at x = \[-\] 2 is 0.
Since f(x) can be enlarged, the maximum value does not exist, which is evident in the graph also.
Hence, the function f does not have a maximum value.
APPEARS IN
RELATED QUESTIONS
f(x) = | sin 4x+3 | on R ?
f(x)=2x3 +5 on R .
f (x) = \[-\] | x + 1 | + 3 on R .
f(x) = 16x2 \[-\] 16x + 28 on R ?
f(x) = x3 \[-\] 3x .
f(x) = cos x, 0 < x < \[\pi\] .
f(x) = (x - 1) (x + 2)2.
`f(x) = 2/x - 2/x^2, x>0`
f(x) = xex.
`f(x) = (x+1) (x+2)^(1/3), x>=-2` .
f(x) = (x \[-\] 1) (x \[-\] 2)2.
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 \[-\] 1)2 + 3 in [ \[-\] 3,1] ?
`f(x) = 3x^4 - 8x^3 + 12x^2- 48x + 25 " in "[0,3]` .
Find the absolute maximum and minimum values of a function f given by \[f(x) = 2 x^3 - 15 x^2 + 36x + 1 \text { on the interval } [1, 5]\] ?
Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
A beam is supported at the two end and is uniformly loaded. The bending moment M at a distance x from one end is given by \[M = \frac{Wx}{3}x - \frac{W}{3}\frac{x^3}{L^2}\] .
Find the point at which M is maximum in a given case.
A tank with rectangular base and rectangular sides, open at the top, is to the constructed so that its depth is 2 m and volume is 8 m3. If building of tank cost 70 per square metre for the base and Rs 45 per square metre for sides, what is the cost of least expensive tank?
Show that the height of the cylinder of maximum volume that can be inscribed a sphere of radius R is \[\frac{2R}{\sqrt{3}} .\]
Determine the points on the curve x2 = 4y which are nearest to the point (0,5) ?
Find the maximum slope of the curve y = \[- x^3 + 3 x^2 + 2x - 27 .\]
Manufacturer can sell x items at a price of rupees \[\left( 5 - \frac{x}{100} \right)\] each. The cost price is Rs \[\left( \frac{x}{5} + 500 \right) .\] Find the number of items he should sell to earn maximum profit.
The total area of a page is 150 cm2. The combined width of the margin at the top and bottom is 3 cm and the side 2 cm. What must be the dimensions of the page in order that the area of the printed matter may be maximum?
Write the point where f(x) = x log, x attains minimum value.
Find the least value of f(x) = \[ax + \frac{b}{x}\], where a > 0, b > 0 and x > 0 .
Write the maximum value of f(x) = \[\frac{\log x}{x}\], if it exists .
If \[ax + \frac{b}{x} \frac{>}{} c\] for all positive x where a,b,>0, then _______________ .
The minimum value of \[\frac{x}{\log_e x}\] is _____________ .
Let f(x) = x3+3x2 \[-\] 9x+2. Then, f(x) has _________________ .
The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .
If x+y=8, then the maximum value of xy is ____________ .
The minimum value of \[\left( x^2 + \frac{250}{x} \right)\] is __________ .
Let x, y be two variables and x>0, xy=1, then minimum value of x+y is _______________ .
The sum of the surface areas of a cuboid with sides x, 2x and \[\frac{x}{3}\] and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of sphere. Also find the minimum value of the sum of their volumes.
Of all the closed right circular cylindrical cans of volume 128π cm3, find the dimensions of the can which has minimum surface area.
Which of the following graph represents the extreme value:-
