Advertisements
Advertisements
प्रश्न
f (x) = \[-\] | x + 1 | + 3 on R .
Advertisements
उत्तर
Given: f(x) =\[- \left| x + 1 \right|\] + 3
Now,
\[- \left| x + 1 \right| \leq 0\] for all x \[\in\] R.
\[\left| x + 1 \right| = 0 . \]
\[ \Rightarrow x = - 1\]
Therefore, the maximum value of f at x = -1 is 3.
Since f(x) can be reduced, the minimum value does not exist, which is evident in the graph also.
Hence, the function f does not have a minimum value.
APPEARS IN
संबंधित प्रश्न
f(x) = 4x2 + 4 on R .
f(x)=| x+2 | on R .
f(x) = | sin 4x+3 | on R ?
f(x) = x3 (x \[-\] 1)2 .
f(x) = \[\frac{1}{x^2 + 2}\] .
f(x) = x3 \[-\] 6x2 + 9x + 15 .
`f(x)=2sinx-x, -pi/2<=x<=pi/2`
f(x) = x4 \[-\] 62x2 + 120x + 9.
`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 \[-\] 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 ?
Prove that f(x) = sinx + \[\sqrt{3}\] cosx has maximum value at x = \[\frac{\pi}{6}\] ?
Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
Divide 15 into two parts such that the square of one multiplied with the cube of the other 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.
Find the largest possible area of a right angled triangle whose hypotenuse is 5 cm long.
Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is \[6\sqrt{3}\]r.
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).
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?
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?
The space s described in time t 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 necessary condition for a point x = c to be an extreme point of the function f(x).
If f(x) attains a local minimum at x = c, then write the values of `f' (c)` and `f'' (c)`.
The minimum value of \[\frac{x}{\log_e x}\] is _____________ .
For the function f(x) = \[x + \frac{1}{x}\]
The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .
At x= \[\frac{5\pi}{6}\] f(x) = 2 sin 3x + 3 cos 3x is ______________ .
The point on the curve y2 = 4x which is nearest to, the point (2,1) is _______________ .
If x+y=8, then the maximum value of xy is ____________ .
f(x) = \[\sin + \sqrt{3} \cos x\] is maximum when x = ___________ .
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 ______________ .
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 minimum value of the function `f(x)=2x^3-21x^2+36x-20` is ______________ .
