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) = - (x-1)2+2 on R ?
f(x) = x3 \[-\] 3x.
f(x) = x3 (x \[-\] 1)2 .
f(x) = \[\frac{1}{x^2 + 2}\] .
f(x) = x3 \[-\] 6x2 + 9x + 15 .
f(x) = sin x \[-\] cos x, 0 < x < 2\[\pi\] .
`f(x)=2sinx-x, -pi/2<=x<=pi/2`
f(x) =\[x\sqrt{1 - x} , x > 0\].
f(x) =\[\frac{x}{2} + \frac{2}{x} , x > 0\] .
f(x) = xex.
`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) = \[x\sqrt{2 - x^2} - \sqrt{2} \leq x \leq \sqrt{2}\] .
`f(x)=xsqrt(1-x), x<=1` .
If f(x) = x3 + ax2 + bx + c has a maximum at x = \[-\] 1 and minimum at x = 3. Determine a, b and c ?
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]` .
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.
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.
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.
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 curve y2 = 4x which is nearest to the point (2,\[-\] 8).
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 strength of a beam varies as the product of its breadth and square of its depth. Find the dimensions of the strongest beam which can be cut from a circular log of radius a ?
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) = \[x + \frac{1}{x}, x > 0 .\]
The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .
The number which exceeds its square by the greatest possible quantity is _________________ .
The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .
The function f(x) = \[\sum^5_{r = 1}\] (x \[-\] r)2 assumes minimum value at x = ______________ .
The least value of the function f(x) = \[x3 - 18x2 + 96x\] in the interval [0,9] is _____________ .
If(x) = x+\[\frac{1}{x}\],x > 0, then its greatest value is _______________ .
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 the function `f(x)=2x^3-21x^2+36x-20` is ______________ .
Which of the following graph represents the extreme value:-
