EASY
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If the minimum and maximum value of function 3x4-8x3+12x2-48x+25 on the interval 0,3 is b and a respectively, then the value a-b is

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Important Questions on Application of Derivatives

HARD
If the function f given by fx=x3-3a-2x2+3ax+7, for some aR is increasing in 0, 1 and decreasing in 1, 5, then a root of the equation, fx-14x-12=0, x1 is :
EASY
Let M and m be respectively the absolute maximum and the absolute minimum values of the function, fx=2x3-9x2+12x+5 in the interval [0,3] . Then M-m is equal to
HARD

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8:15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are:

MEDIUM
The least value of αR for which, 4αx2+1x 1, for all x>0, is 
MEDIUM
If x=-1 and x=2 are extreme points of fx=αlogx+βx2+x, then 
HARD
The function fx=2x+x+2-x+2-2x has a local minimum or a local maximum at x=
EASY
The maximum value of the function fx=2x3-15x2+36x+4 is attained at
HARD
Let fx=x2+1x2 and gx=x-1x, xR--1, 0, 1. If hx=fxgx , then the local minimum value of hx is:
 
HARD
A solid hemisphere is mounted on a solid cylinder, both having equal radii. If the whole solid is to have a fixed surface area and the maximum possible volume, then the ratio of the height of the cylinder to the common radius is
MEDIUM
Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is:
HARD
Let fx=α x2-2+1x where α is a real constant. The smallest α for which fx0 for all x>0 is-
MEDIUM
From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration g=32 m/s2, is:
HARD
Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e., the angle between the bounding radii) is-
HARD
The maximum area (in sq. units) of a rectangle having its base on the x- axis and its other two vertices on the parabola, y=12-x2 such that the rectangle lies inside the parabola, is :
MEDIUM
If non-zero real numbers b and c are such that  min fx>max gx, where fx=x2+2bx+2c2 and gx=-x2-2cx+b2, xR; then cb lies in the interval 
MEDIUM
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side =x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then
HARD
For every pair of continuous functions f, g :0, 1R such that maxfx: x0, 1=max{gx: x0, 1}, then the correct statement(s) is(are)
HARD
The maximum value of fx=logxx (x0,x1) is
HARD
Let k and K be the minimum and the maximum values of the function fx=1+x0.61+x0.6 in 0, 1, respectively, then the ordered pair (k, K) is equal to:
HARD
The maximum value of fx=x4+x+x2 on [-1, 1] is