The lower corner of a leaf in a book is folded over so as to just reach the inner edge of the page. The fraction of width folded over if the area of the folded part is minimum is
If x_{1} and x_{2} are abscissa of two points on the curve f(x) = x – x^{2} in the interval [0, 1], then maximum value of the expression (x_{1} + x_{2}) – is
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Least value of the function, f(x)= is
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is
The coordinate of the point for minimum value of z = 7x – 8y subject to the conditions x + y – 20 £ 0, y ³ 5, x ³ 0, y ³ 0
The equation x^{3} – 3x + [a] = 0, will have three real and distinct roots if
(where [*] denotes the greatest integer function)
Let f(x) = . Then the set of values of a for which f can attain its maximum values is
(where a>0 and { * } denotes the fractional part function)
A function is defined as f(x) = ax^{2} – bx where a and b are constants then at x = 0 we will have a maxima of f(x) if
A and B are the points (2, 0) and (0, 2) respectively. The coordinates of the point P on the line 2x+3y+1=0 are
The maximum value of f(x) = 2bx^{2} – x^{4} – 3b is g(b), where b > 0, if b varies then the minimum value of g(b) is
Number of solution(s) satisfying the equation, 3x^{2} – 2x^{3} = log_{2} (x^{2} + 1) – log_{2} x is
If a^{2}x^{4} + b^{2} y^{4} = c^{6}, then the maximum value of xy is
Maximum and minimum value of f(x) = max (sin t), 0 < t < x, 0 £ x £ 2p are
The function `f' is defined by f(x) = x^{p} (1 – x)^{q} for all x Î R, where p, q are positive integers, has a maximum value, for x equal to
The maximum slope of the curve y=–x^{3}+3x^{2}+2x–27 will be
Two points A(1, 4) & B(3, 0) are given on the ellipse 2x^{2} + y^{2} = 18. The coordinates of a point C on the ellipse such that the area of the triangle ABC is greatest is
The lateral edge of a regular hexagonal pyramid is 1 cm. If the volume is maximum, then its height must be equal to
Let f(x) = 5x – 2x^{2} + 2; x ∈ N then the maximum value of f(x) is
The maximum value of f(x), if f(x) + , x ∈ domain of f
204 videos288 docs139 tests

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 
NCERT Exemplar: Application of Derivatives 2 Doc  14 pages 
Important Formulas: Application of Derivatives Formulas Doc  12 pages 
Test: Application of Derivatives Assertion & Reason Type Questions Test  15 ques 
204 videos288 docs139 tests

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 
NCERT Exemplar: Application of Derivatives 2 Doc  14 pages 
Important Formulas: Application of Derivatives Formulas Doc  12 pages 
Test: Application of Derivatives Assertion & Reason Type Questions Test  15 ques 