Application of Derivatives questions
910 published questions with worked solutions.
- The total number of local maxima and local minima of the function f(x) = cases (2+x)^3, & -3 < x -1 x^ 2/3 , & -1 < x < 2 cases is
- Let f(x) be a non-constant twice differentiable function defined on (- , ) such that f(x) = f(1-x) and f' ( 1 4 ) = 0. Then,
- The real number k for which the equation, 2x^3 + 3x + k = 0 has two distinct real roots in [0, 1]
- The intercepts on x-axis made by tangents to the curve, y = _0^x |t| ,dt, x R, which are parallel to the line y = 2x, are equal...
- Let f : R R be a twice differentiable function such that f''(x) > 0 for all x R and f'(a-1) = 0, where a is a real number. Let...
- Let f(x) = x^ 2025 - x^ 2000 , x [0, 1] and the minimum value of the function f(x) in the interval [0, 1] be (80)^ 80 (n)^ -81 ....
- The least value of ( ^2 - 6 + 3 ^2 + 2) is
- Let f be a differentiable function satisfying f(x)=1-2x+ _0^x e^ (x-t) f(t)dt, x R and let g(x)= _0^x (f(t)+2)^ 15 (t-4)^6(t+12)^...
- Let f(x) = _0^ x^2 t^2-8t+15 e^t ,dt, x R . Then the number of local maximum and local minimum points of f, respectively, are :
- If the set of all values of a, for which the equation 5x^3 - 15x - a = 0 has three distinct real roots, is the interval (α, β),...
- Consider the region R = (x, y): x y 9 - 11 3 x^2, x 0 . The area, of the largest rectangle of sides parallel to the coordinate...
- Let (2, 3) be the largest open interval in which the function f(x) = 2 _e(x - 2) - x^2 + ax + 1 is strictly increasing and (b, c)...
- The sum of all local minimum values of the function f(x) = cases 11 18 (x-4)(x-5), & x > 2 1 3 (7+2|x|), & -1 x 2 1-2x, & x < -1...
- If the function f(x) = 2x^3 - 9ax^2 + 12a^2x + 1, where a > 0, attains its local maximum and local minimum values at p and q,...
- Let f: R R be a function defined by f(x) = ||x+2| - 2|x||. If m is the number of points of local minima and n is the number of...
- Let the function f(x) = x 3 + 3 x +3, x 0 be strictly increasing in (- , _1) ( _2, ) and strictly decreasing in ( _3, _4) ( _4,...
- Let f be a differentiable function on R such that f(2) =1, f '(2) = 4. Let _ x 0 (f(2 + x))^ 3/x = e^ . Then the number of times...
- Let f : R → R be a polynomial function of degree four having extreme values at x = 4 and x = 5. If _ x 0 f(x) x^2 = 5, then f(2)...
- For real x, let f(x)=x^3+5x+1. Then
- The function f:R R is defined by f(x)=3^ -x . Observe the following statements: I. f is one-one; II. f is onto; III. f is a...
Page 1Next
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