हिंदी

Prove that the following function do not have maxima or minima: g(x) = logx

Advertisements
Advertisements

प्रश्न

Prove that the following function do not have maxima or minima:

g(x) = logx

योग
Advertisements

उत्तर

Given function g(x) = log x

∴ g'(x) = `1/x, x > 0`

`g (x) = 1/x ne 0` for all x ∈ (0, ∞)

⇒ x ∈ R, g'(x) is never equal to zero.

Hence there is no highest or lowest value of g.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.5 [पृष्ठ २३२]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.5 | Q 4.2 | पृष्ठ २३२

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is π/3.


Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`. Also find maximum volume in terms of volume of the sphere


Find the maximum and minimum value, if any, of the following function given by f(x) = 9x2 + 12x + 2


Find the maximum and minimum value, if any, of the function given by f(x) = |x + 2| − 1.


Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

`f(x) = 4x - 1/x x^2, x in [-2 ,9/2]`


Find two numbers whose sum is 24 and whose product is as large as possible.


Find two positive numbers x and y such that their sum is 35 and the product x2y5 is a maximum.


Show that the right circular cylinder of given surface and maximum volume is such that is heights is equal to the diameter of the base.


Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is `8/27` of the volume of the sphere.


For all real values of x, the minimum value of `(1 - x + x^2)/(1+x+x^2)` is ______.


Find the absolute maximum and minimum values of the function f given by f (x) = cos2 x + sin x, x ∈ [0, π].


Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.


The total cost of producing x units is ₹ (x2 + 60x + 50) and the price is ₹ (180 − x) per unit. For what units is the profit maximum?


Divide the number 20 into two parts such that their product is maximum


If f(x) = px5 + qx4 + 5x3 - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = ______.


If f(x) = `x + 1/x, x ne 0`, then local maximum and x minimum values of function f are respectively.


The maximum and minimum values for the function f(x) = 4x3 - 6x2 on [-1, 2] are ______


Let f have second derivative at c such that f′(c) = 0 and f"(c) > 0, then c is a point of ______.


A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs 300/- per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Re 1/- one subscriber will discontinue the service. Find what increase will bring maximum profit?


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. Also, find the maximum volume.


AB is a diameter of a circle and C is any point on the circle. Show that the area of ∆ABC is maximum, when it is isosceles.


The smallest value of the polynomial x3 – 18x2 + 96x in [0, 9] is ______.


The curves y = 4x2 + 2x – 8 and y = x3 – x + 13 touch each other at the point ______.


Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x2.


The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are ____________.


For all real values of `x`, the minimum value of `(1 - x + x^2)/(1 + x + x^2)`


A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is ______.


The set of values of p for which the points of extremum of the function f(x) = x3 – 3px2 + 3(p2 – 1)x + 1 lie in the interval (–2, 4), is ______.


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 ______.


The greatest value of the function f(x) = `tan^-1x - 1/2logx` in `[1/sqrt(3), sqrt(3)]` is ______.


A straight line is drawn through the point P(3, 4) meeting the positive direction of coordinate axes at the points A and B. If O is the origin, then minimum area of ΔOAB is equal to ______.


A metal wire of 36 cm long is bent to form a rectangle. Find its dimensions when its area is maximum.


A right circular cylinder is to be made so that the sum of the radius and height is 6 metres. Find the maximum volume of the cylinder.


If \[\mathrm{A}+\mathrm{B}=\frac{\pi}{2}\] then the maximum value of cosA.cosB is


The absolute maximum value of the function f(x) = 2x3 − 3x2 − 36x + 9 defined on [−3, 3] is ______.


For a function defined on an interval \[I\], which condition means that \[f\] has a minimum value at \[c\in I\]?


For \[f(x)=3x^4+4x^3-12x^2+12\], what conclusion follows at \[x=-2\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×