Advertisements
Advertisements
प्रश्न
f(x) = x3 \[-\] 1 on R .
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)=| x+2 | on R .
f(x)=sin 2x+5 on R .
f(x) = \[\frac{1}{x^2 + 2}\] .
f(x) = sin x \[-\] cos x, 0 < x < 2\[\pi\] .
`f(x)=sin2x-x, -pi/2<=x<=pi/2`
`f(x) = 2/x - 2/x^2, x>0`
f(x) = xex.
f(x) = \[x + \frac{a2}{x}, a > 0,\] , x ≠ 0 .
Show that \[\frac{\log x}{x}\] has a maximum value at x = e ?
Find the maximum and minimum values of the function f(x) = \[\frac{4}{x + 2} + x .\]
Find the maximum and minimum values of y = tan \[x - 2x\] .
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 maximum value of 2x3\[-\] 24x + 107 in the interval [1,3]. Find the maximum value of the same function in [ \[-\] 3, \[-\] 1].
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]` .
Determine two positive numbers whose sum is 15 and the sum of whose squares is maximum.
Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
Two sides of a triangle have lengths 'a' and 'b' and the angle between them is \[\theta\]. What value of \[\theta\] will maximize the area of the triangle? Find the maximum area of the triangle also.
A window in the form of a rectangle is surmounted by a semi-circular opening. The total perimeter of the window is 10 m. Find the dimension of the rectangular of the window to admit maximum light through the whole opening.
A rectangle is inscribed in a semi-circle of radius r with one of its sides on diameter of semi-circle. Find the dimension of the rectangle so that its area is maximum. Find also the area ?
Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm ?
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 point on the parabolas x2 = 2y which is closest to the point (0,5) ?
Find the point on the curvey y2 = 2x which is at a minimum distance from the point (1, 4).
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?
A particle is moving in a straight line such that its distance at any time t is given by S = \[\frac{t^4}{4} - 2 t^3 + 4 t^2 - 7 .\] Find when its velocity is maximum and acceleration minimum.
Write necessary condition for a point x = c to be an extreme point of the function f(x).
Write the point where f(x) = x log, x attains minimum value.
Let f(x) = (x \[-\] a)2 + (x \[-\] b)2 + (x \[-\] c)2. Then, f(x) has a minimum at x = _____________ .
The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .
The maximum value of f(x) = \[\frac{x}{4 - x + x^2}\] on [ \[-\] 1, 1] is _______________ .
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 _________________ .
f(x) = 1+2 sin x+3 cos2x, `0<=x<=(2pi)/3` is ________________ .
The minimum value of x loge x is equal to ____________ .
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?
Of all the closed right circular cylindrical cans of volume 128π cm3, find the dimensions of the can which has minimum surface area.