Application of Derivatives questions
910 published questions with worked solutions.
- Let S be the set of all natural numbers, for which the line x/a + y/b = 2 is a tangent to the curve (x/a)^ n + (y/b)^ n = 2 at...
- Let the normal at the point P on the parabola y^ 2 = 6x pass through the point (5, −8). If the tangent at P to the parabola...
- Let f(x) = 2 ^ -1 x + 4 ^ -1 x - 3x^ 2 - 2x + 10, x [−1, 1]. If [a, b] is the range of the function f then 4a − b is equal to :
- Let f(x) = max |x + 1|, |x + 2|, ......., |x + 5| . Then _ -6 ^0f(x)dx is equal to _____.
- An angle of intersection of the curves, x^2 a^2 + y^2 b^2 =1 and x^2+y^2=ab, a > b, is :
- Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then
- Let f(x) be a cubic polynomial with f(1) = –10, f(–1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x =...
- The sum of absolute maximum and minimum values of the function f(x) = |x^2-5x+6|-3x+2 in the interval [–1, 3] is equal to :
- Let f(x) = vmatrix 1+ ^2x& ^2x& 2x ^2x&1+ ^2x& 2x ^2x& ^2x&1+ 2x vmatrix , x [ 6 , 3 ]. If and respectively are the maximum and...
- Let f (x) = 2x + ^ -1 x and g(x) = _e ( 1+x^2 +x ), x [0, 3]. Then
- Let a curve y = f(x), x (0, ) pass through the points P (1, 3 2 ) and Q (a, 1 2 ). If the tangent at any point R(b, f(b)) to the...
- The number of points, where the curve y = x^5-20x^3+50x+2 crosses the x-axis, is __________.
- Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^ x^2 + e^ -x^2 , g(x) = xe^ x^2 + e^ -x^2 and...
- The maximum value of the expression 1 ^2 + 3 + 5 ^2 is
- Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the...
- Let f be a function defined on R (the set of all real numbers) such that f'(x) = 2010(x - 2009)(x - 2010)^2(x - 2011)^3(x -...
- The minimum value of the sum of real numbers a^ -5 , a^ -4 , 3a^ -3 , 1, a^8 and a^ 10 with a > 0 is
- The number of distinct real roots of x^4 - 4x^3 + 12x^2 + x - 1 = 0 is
- The function f : [0, 3] [1, 29], defined by f(x) = 2x^3 - 15x^2 + 36x + 1, is
- Let f : R R be defined as f(x) = |x| + |x^2 - 1|. The total number of points at which f attains either a local maximum or a local...
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and IntegrationChemical Kinetics