Advertisements
Advertisements
प्रश्न
f(x) = \[\frac{1}{x^2 + 2}\] .
Advertisements
उत्तर
\[\text { Given }: \hspace{0.167em} f\left( x \right) = \frac{1}{x^2 + 2}\]
\[ \Rightarrow f'\left( x \right) = \frac{- 2x}{\left( x^2 + 2 \right)^2}\]
\[\text { For the local maxima or minima, we must have }\]
\[ f'\left( x \right) = 0\]
\[ \Rightarrow \frac{- 2x}{\left( x^2 + 2 \right)^2} = 0\]
\[ \Rightarrow x = 0\]
Now, for values close to x = 0 and to the left of 0,
APPEARS IN
संबंधित प्रश्न
f(x) = | sin 4x+3 | on R ?
f(x) = x3 \[-\] 3x.
f(x) = sin x \[-\] cos x, 0 < x < 2\[\pi\] .
Find the point of local maximum or local minimum, if any, of the following function, using the first derivative test. Also, find the local maximum or local minimum value, as the case may be:
f(x) = x3(2x \[-\] 1)3.
f(x) =\[\frac{x}{2} + \frac{2}{x} , x > 0\] .
f(x) = x4 \[-\] 62x2 + 120x + 9.
f(x) = x3\[-\] 6x2 + 9x + 15
`f(x) = 2/x - 2/x^2, x>0`
`f(x)=xsqrt(32-x^2), -5<=x<=5` .
f(x) = \[x + \sqrt{1 - x}, x \leq 1\] .
f(x) = (x \[-\] 1) (x \[-\] 2)2.
f(x) = 4x \[-\] \[\frac{x^2}{2}\] in [ \[-\] 2,4,5] .
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 the function of given by \[f(x) = \cos^2 x + \sin x, x \in [0, \pi]\] .
Find the absolute maximum and minimum values of a function f given by f(x) = 2x3 − 15x2 + 36x + 1 on the interval [1, 5].
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.
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?
Show that the height of the cylinder of maximum volume that can be inscribed a sphere of radius R is \[\frac{2R}{\sqrt{3}} .\]
An isosceles triangle of vertical angle 2 \[\theta\] is inscribed in a circle of radius a. Show that the area of the triangle is maximum when \[\theta\] = \[\frac{\pi}{6}\] .
Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius \[5\sqrt{3 cm} \text { is }500 \pi {cm}^3 .\]
Determine the points on the curve x2 = 4y which are nearest to the point (0,5) ?
Find the point on the curvey y2 = 2x which is at a minimum distance from the point (1, 4).
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.
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 necessary condition for a point x = c to be an extreme point of the function f(x).
Write the minimum value of f(x) = xx .
The maximum value of x1/x, x > 0 is __________ .
If \[ax + \frac{b}{x} \frac{>}{} c\] for all positive x where a,b,>0, then _______________ .
The function f(x) = \[\sum^5_{r = 1}\] (x \[-\] r)2 assumes minimum value at x = ______________ .
If x lies in the interval [0,1], then the least value of x2 + x + 1 is _______________ .
The least value of the function f(x) = \[x3 - 18x2 + 96x\] in the interval [0,9] is _____________ .
The minimum value of \[\left( x^2 + \frac{250}{x} \right)\] is __________ .
If(x) = x+\[\frac{1}{x}\],x > 0, then its greatest value is _______________ .
The function f(x) = \[2 x^3 - 15 x^2 + 36x + 4\] is maximum at x = ________________ .
The maximum value of f(x) = \[\frac{x}{4 + x + x^2}\] on [ \[-\] 1,1] is ___________________ .
Which of the following graph represents the extreme value:-
