Advertisements
Advertisements
प्रश्न
Write necessary condition for a point x = c to be an extreme point of the function f(x).
Advertisements
उत्तर
We know that at the extreme points of a function f(x), the first order derivative of the function is equal to zero, i.e.
`f'(x) = 0 " at " x = c`
`⇒ f'(c) = 0`
APPEARS IN
संबंधित प्रश्न
f(x)=2x3 +5 on R .
f(x) = 16x2 \[-\] 16x + 28 on R ?
f(x) = x3 \[-\] 1 on R .
f(x) = (x \[-\] 5)4.
f(x) = (x \[-\] 1) (x+2)2.
f(x) = sin 2x, 0 < x < \[\pi\] .
f(x) =\[\frac{x}{2} + \frac{2}{x} , x > 0\] .
f(x) = xex.
f(x) = \[x + \sqrt{1 - x}, x \leq 1\] .
Find the maximum and minimum values of y = tan \[x - 2x\] .
Prove that f(x) = sinx + \[\sqrt{3}\] cosx has maximum value at x = \[\frac{\pi}{6}\] ?
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].
A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Find this maximum volume.
Prove that a conical tent of given capacity will require the least amount of canavas when the height is \[\sqrt{2}\] times the radius of the base.
Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm ?
Find the point on the curve y2 = 4x which is nearest to the point (2,\[-\] 8).
Find the point on the curve x2 = 8y which is nearest to the point (2, 4) ?
Find the point on the parabolas x2 = 2y which is closest to the point (0,5) ?
Find the maximum slope of the curve y = \[- x^3 + 3 x^2 + 2x - 27 .\]
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 sufficient conditions for a point x = c to be a point of local maximum.
Write the maximum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]
Write the point where f(x) = x log, x attains minimum value.
Find the least value of f(x) = \[ax + \frac{b}{x}\], where a > 0, b > 0 and x > 0 .
For the function f(x) = \[x + \frac{1}{x}\]
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 ______________ .
At x= \[\frac{5\pi}{6}\] f(x) = 2 sin 3x + 3 cos 3x is ______________ .
The least value of the function f(x) = \[x3 - 18x2 + 96x\] in the interval [0,9] is _____________ .
The point on the curve y2 = 4x which is nearest to, the point (2,1) is _______________ .
The minimum value of \[\left( x^2 + \frac{250}{x} \right)\] is __________ .
The function f(x) = \[2 x^3 - 15 x^2 + 36x + 4\] is maximum at x = ________________ .
