f(x) = 1 + 2x^{2} + 4x^{4} + 6x^{6} + ................+ 100x^{100} is polynomial in a real variable x, then f(x) has
On the interval [0, 1] the function x^{25}(1 – x)^{75} takes its maximum value at
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The product of minimum value of x^{x} and maximum value of is
The minimum value of the function defined by f(x) = max (x, x + 1, 2 – x) is
The greatest and the least values of the function, f(x) = 2 – , x ∈ [–2, 1] are
Let f(x) = {x}, For f(x), x = 5 is (where {*} denotes the fractional part)
The difference between the greatest and least values of the function f(x) = sin 2x – x on [–p/2, p/2] is
The radius of a right circular cylinder of greatest curved surface which can be inscribed in a given right circular cone is
The dimensions of the rectangle of maximum area that can be inscribed in the ellipse (x/4)^{2} + (y/3)^{2} = 1 are
The largest area of a rectangle which has one side on the x–axis and the two vertices on the curve y = is
The co–ordinates of the point on the curve x^{2} = 4y, which is at least distance from the line
y = x – 4 is
Let f(x) = the set of values of b for which f(x) has greatest value at x = 1 is given by
The set of values of p for which the extrema of the function, f(x) = x^{3} – 3px^{2} + 3(p^{2} – 1) x + 1 lie in the interval (–2, 4) is
Four points A, B, C, D lie in that order on the parabola y = ax^{2} + bx + c. The co–ordinates of A, B & D are known as A(–2, 3); B(–1, 1) and D(2, 7). The co–ordinates of C for which the area of the quadrilateral ABCD is greatest is
In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is l. The altitude of the prism for which the volume is greatest is
Two vertices of a rectangle are on the positive x–axis. The other two vertices lie on the lines y = 4x and y = –5x + 6. Then the maximum area of the rectangle is
A variable point P is chosen on the straight line x + y = 4 and tangents PA and PB are drawn from it to circle x^{2} + y^{2} = 1. Then the position of P for the smallest length of chord of contact AB is
The maximum area of the rectangle whose sides pass through the angular points of a given rectangle of sides a and b is
If p and q are positive real numbers such that p^{2} + q^{2} = 1, then the maximum value of (p + q) is
The function f(x) = has a local minimum at
If the function f(x) = 2x^{3} – 9ax^{2} + 12a^{2}x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p^{2} = q, then a equals
The maximum value x^{3} – 3x in the interval [0, 2] is
The minimum value of (x – p)^{2} + (x – q)^{2} + (x – r)^{2} will be at x equals to
The number of values of x where f(x) = cos x + cos x attains its maximum value is
The maximum value of cos a_{1} . cos a_{2} . cos a_{3}....cos a_{n} under the restriction 0 £ a_{1}, a_{2},.....a_{n} £and cot a_{1} cot a_{2 }.... cot a_{n}=1 is
204 videos288 docs139 tests

Finding maxima and minima Using First Derivative Test (with Example) Video  09:27 min 
Examples: Rate of change of quantities Video  11:50 min 
JEE Advanced Level Test: Maxima and Minima 2 Test  19 ques 
Finding maxima and Minima Using Second Derivative Test (with Example) Video  08:15 min 
Maximum and Minimum Value of a Function in a Closed Interval Video  12:27 min 
204 videos288 docs139 tests

Finding maxima and minima Using First Derivative Test (with Example) Video  09:27 min 
Examples: Rate of change of quantities Video  11:50 min 
JEE Advanced Level Test: Maxima and Minima 2 Test  19 ques 
Finding maxima and Minima Using Second Derivative Test (with Example) Video  08:15 min 
Maximum and Minimum Value of a Function in a Closed Interval Video  12:27 min 