Application of Derivatives questions
910 published questions with worked solutions.
- The number of positive real roots of x^4 - 4x - 1 = 0, is
- Let n be an odd positive integer. Then, the number of real roots of the polynomial P_n(x) = 1 + 2x + 3x^2 + + (n+1)x^n, is
- Let P_n(x) = 1 + 2x + 3x^2 + + (n+1)x^n be a polynomial such that n is even. Then, the number of real roots of P_n(x), is
- The approximate value of [3] 28 is
- The number of real roots of f(x)=0, where f(x)=(x-1)(x-2)(x-3)(x-4) lying in the interval (1,3) is
- If , and are the roots of the equation x^3-3x+1=0, then [ ]+[ ]+[ ] is ([ ] denotes the greatest integer function)
- If the cubic 2x^3-9x^2+12x+k=0 has two equal roots, then maximum value of |k| is
- If a,b,c are non-zero real numbers, then the minimum value of the expression ( (a^4+3a^2+1 ) (b^4+5b^2+1 ) (c^4+7c^2+1 )...
- Let a,b and c be distinct non zero real numbers such that 1-a^3 a= 1-b^3 b= 1-c^3 c. The value of (a^3+b^3+c^3 ), is
- If the equation x^3-3x+a=0 has distinct roots between 0 and 1, then the value of a is
- If a and b are two distinct real roots of the polynomial f(x) such that a<b, then there exists a real number c lying between a...
- If the equation x^3+ax^2+b=0, b 0 has a root of order 2, then
- If x=c is a root of order 2 of a polynomial f(x), then x=c is also a root of the polynomial
- The real number k for which the equation 2x^3+3x+k=0 has two distinct real roots in [0,1]
- The value of such that sum of the squares of the roots of the quadratic equation, x^2+(3- )x+2= has the least value is
- Let f(x) be a polynomial of degree 5, and have extrema at x = 1 and x = −1. If _ x 0 ( f(x) x^3 ) = -5, then f(2) − f(−2) is...
- The number of critical points of the function f(x) = cases | x x |, & x 0 1, & x = 0 cases in the interval (−2π, 2π) is equal to:
- _ 0 x (16 ( x2 ) ^3 ( x2 ) ) is equal to:
- Let (2^(1−a)+2^(1+a)), f(a), (3^a+3^(−a)) be in A.P. and α be the minimum value of f(a). Then the value of the integral _ _e( -1)...
- The sum of all the integral values of p such that the equation 3sin²x+12cosx−3=p, x∈ℝ, has at least one solution, is:
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