Advertisements
Advertisements
प्रश्न
f(x) = x3 \[-\] 1 on R .
Advertisements
उत्तर

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.
APPEARS IN
संबंधित प्रश्न
f(x)=sin 2x+5 on R .
f(x)=2x3 +5 on R .
f(x) = 16x2 \[-\] 16x + 28 on R ?
f(x) = \[\frac{1}{x^2 + 2}\] .
f(x) = x3 \[-\] 6x2 + 9x + 15 .
f(x) = cos x, 0 < x < \[\pi\] .
`f(x)=sin2x-x, -pi/2<=x<=pi/2`
f(x) =\[\frac{x}{2} + \frac{2}{x} , x > 0\] .
f(x) = x4 \[-\] 62x2 + 120x + 9.
`f(x) = 2/x - 2/x^2, x>0`
f(x) = \[x + \sqrt{1 - x}, x \leq 1\] .
Find the maximum and minimum values of the function f(x) = \[\frac{4}{x + 2} + x .\]
f(x) = 4x \[-\] \[\frac{x^2}{2}\] in [ \[-\] 2,4,5] .
Find the absolute maximum and minimum values of a function f given by `f(x) = 12 x^(4/3) - 6 x^(1/3) , x in [ - 1, 1]` .
Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
How should we choose two numbers, each greater than or equal to `-2, `whose sum______________ so that the sum of the first and the cube of the second is minimum?
Of all the closed cylindrical cans (right circular), which enclose a given volume of 100 cm3, which has the minimum surface area?
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 rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, in cutting off squares from each corners and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum possible?
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.
Show that the height of the cylinder of maximum volume that can be inscribed a sphere of radius R is \[\frac{2R}{\sqrt{3}} .\]
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 ?
Find the point on the curve y2 = 4x which is nearest to the point (2,\[-\] 8).
Find the point on the parabolas x2 = 2y which is closest to the point (0,5) ?
The total cost of producing x radio sets per day is Rs \[\left( \frac{x^2}{4} + 35x + 25 \right)\] and the price per set at which they may be sold is Rs. \[\left( 50 - \frac{x}{2} \right) .\] Find the daily output to maximum the total profit.
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.
Write necessary condition for a point x = c to be an extreme point of the function f(x).
Write sufficient conditions for a point x = c to be a point of local maximum.
If f(x) attains a local minimum at x = c, then write the values of `f' (c)` and `f'' (c)`.
Write the maximum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]
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 .
The least and greatest values of f(x) = x3\[-\] 6x2+9x in [0,6], are ___________ .
Let x, y be two variables and x>0, xy=1, then minimum value of x+y is _______________ .
Let f(x) = 2x3\[-\] 3x2\[-\] 12x + 5 on [ 2, 4]. The relative maximum occurs at x = ______________ .
The minimum value of x loge x is equal to ____________ .
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.
