Advertisements
Advertisements
Question
Write necessary condition for a point x = c to be an extreme point of the function f(x).
Advertisements
Solution
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
RELATED QUESTIONS
f(x) = - (x-1)2+2 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) = 2/x - 2/x^2, x>0`
f(x) = xex.
f(x) = \[x^3 - 2a x^2 + a^2 x, a > 0, x \in R\] .
f(x) = \[x + \sqrt{1 - x}, x \leq 1\] .
`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 ?
Prove that f(x) = sinx + \[\sqrt{3}\] cosx has maximum value at x = \[\frac{\pi}{6}\] ?
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]` .
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?
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 the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm ?
A closed cylinder has volume 2156 cm3. What will be the radius of its base so that its total surface area is minimum ?
Show that among all positive numbers x and y with x2 + y2 =r2, the sum x+y is largest when x=y=r \[\sqrt{2}\] .
Determine the points on the curve x2 = 4y which are nearest to the point (0,5) ?
Find the point on the curve y2 = 4x which is nearest to the point (2,\[-\] 8).
Find the maximum slope of the curve y = \[- x^3 + 3 x^2 + 2x - 27 .\]
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.
Write the maximum value of f(x) = x1/x.
The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .
At x= \[\frac{5\pi}{6}\] f(x) = 2 sin 3x + 3 cos 3x is ______________ .
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 ______________ .
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 _______________ .
f(x) = 1+2 sin x+3 cos2x, `0<=x<=(2pi)/3` is ________________ .
The maximum value of f(x) = \[\frac{x}{4 + x + x^2}\] on [ \[-\] 1,1] is ___________________ .
Let f(x) = 2x3\[-\] 3x2\[-\] 12x + 5 on [ 2, 4]. The relative maximum occurs at x = ______________ .
