Advertisements
Advertisements
प्रश्न
The minimum value of the function `f(x)=2x^3-21x^2+36x-20` is ______________ .
पर्याय
-128
-126
-120
none of these
उत्तर
`-128`
Given:-
`f(x)=2x^3-21x^2+36x-20`
`rArrf'(x)=6x^2-42x+36`
For a local maxima or a local minima, we must have
`f'(x)=0`
`rArr6x^2-42x+36=0`
`rArrx^2-7x+6=0`
`rArr(x-1)(x-6)=0`
`rArrx=1, 6`
Now,
`f''(x)=12x-42`
`rArrf''(1)=12-42=-30<0`
So, x = 1 is a local maxima.
Also,
`f''(6)=72-42=30>0`
So, x = 6 is a local minima.
The local minimum value is given by
`f(6)=2(6)^3-21(6)^2+36(6)-20=-128`
APPEARS IN
संबंधित प्रश्न
f(x)=| x+2 | on R .
f (x) = \[-\] | x + 1 | + 3 on R .
f(x) = x3 (x \[-\] 1)2 .
f(x) = x3 \[-\] 6x2 + 9x + 15 .
`f(x)=sin2x-x, -pi/2<=x<=pi/2`
f(x) = x4 \[-\] 62x2 + 120x + 9.
f(x) = xex.
`f(x)=xsqrt(32-x^2), -5<=x<=5` .
f(x) = \[x\sqrt{2 - x^2} - \sqrt{2} \leq x \leq \sqrt{2}\] .
f(x) = (x \[-\] 2) \[\sqrt{x - 1} \text { in }[1, 9]\] .
Find the absolute maximum and minimum values of the function of given by \[f(x) = \cos^2 x + \sin x, x \in [0, \pi]\] .
Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
Find the largest possible area of a right angled triangle whose hypotenuse is 5 cm long.
A window in the form of a rectangle is surmounted by a semi-circular opening. The total perimeter of the window is 10 m. Find the dimension of the rectangular of the window to admit maximum light through the whole opening.
A rectangle is inscribed in a semi-circle of radius r with one of its sides on diameter of semi-circle. Find the dimension of the rectangle so that its area is maximum. Find also the area ?
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 ?
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 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.
A particle is moving in a straight line such that its distance at any time t is given by S = \[\frac{t^4}{4} - 2 t^3 + 4 t^2 - 7 .\] Find when its velocity is maximum and acceleration minimum.
Write sufficient conditions for a point x = c to be a point of local maximum.
If f(x) attains a local minimum at x = c, then write the values of `f' (c)` and `f'' (c)`.
Write the minimum value of f(x) = xx .
The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .
The number which exceeds its square by the greatest possible quantity 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 _______________ .
f(x) = \[\sin + \sqrt{3} \cos x\] is maximum when x = ___________ .
The minimum value of \[\left( x^2 + \frac{250}{x} \right)\] 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 function f(x) = \[2 x^3 - 15 x^2 + 36x + 4\] is maximum at x = ________________ .
