Advertisements
Advertisements
Question
Write necessary condition for a point x = c to be an extreme point of the function f(x).
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)=2x3 +5 on R .
f(x) = x3 \[-\] 1 on R .
f(x) = (x \[-\] 5)4.
f(x) = x3 (x \[-\] 1)2 .
f(x) =\[x\sqrt{1 - x} , x > 0\].
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) = x3\[-\] 6x2 + 9x + 15
f(x) = (x - 1) (x + 2)2.
f(x) = xex.
`f(x) = (x+1) (x+2)^(1/3), x>=-2` .
Find the maximum and minimum values of y = tan \[x - 2x\] .
Prove that f(x) = sinx + \[\sqrt{3}\] cosx has maximum value at x = \[\frac{\pi}{6}\] ?
Determine two positive numbers whose sum is 15 and the sum of whose squares is maximum.
Divide 15 into two parts such that the square of one multiplied with the cube of the other is minimum.
Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is \[6\sqrt{3}\]r.
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 ?
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 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 = \[- x^3 + 3 x^2 + 2x - 27 .\]
A straight line is drawn through a given point P(1,4). Determine the least value of the sum of the intercepts on the coordinate axes ?
Write sufficient conditions for a point x = c to be a point of local maximum.
Write the minimum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]
Write the minimum value of f(x) = xx .
For the function f(x) = \[x + \frac{1}{x}\]
Let f(x) = x3+3x2 \[-\] 9x+2. Then, f(x) has _________________ .
The number which exceeds its square by the greatest possible quantity is _________________ .
Let f(x) = (x \[-\] a)2 + (x \[-\] b)2 + (x \[-\] c)2. Then, f(x) has a minimum at x = _____________ .
The point on the curve y2 = 4x which is nearest to, the point (2,1) is _______________ .
f(x) = \[\sin + \sqrt{3} \cos x\] is maximum when x = ___________ .
If(x) = x+\[\frac{1}{x}\],x > 0, then its greatest value is _______________ .
f(x) = 1+2 sin x+3 cos2x, `0<=x<=(2pi)/3` 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 ___________________ .
The minimum value of the function `f(x)=2x^3-21x^2+36x-20` is ______________ .
