Lagrange’s Mean Value Theorem MCQ

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• Find point c between where, the slope of tangent to the function f(x) = x2+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)). (Providing given function is continuous and differentiable in given interval).
  ক

  where, the slope of tangent to the function f(x) = x2+3x+2 at point c is equals to the slope of a line joining point (-1,f(-1)) and (6,f(6)). (Providing given function is continuous and differentiable in given interval). ] 2.5

  খ

  -1,6

  গ

  -1,6

  ঘ

  -1,6
• Find the equation of curve whose roots gives the point which lies in the curve f(x) = xSin(x) in the interval where slope of a tangent to a curve is equals to the slope of a line joining (0, π⁄2)
  ক

  where slope of a tangent to a curve is equals to the slope of a line joining (0, π⁄2) ] c = -Sec(c) – Tan(c)

  খ

  0, π⁄2

  গ

  0, π⁄2

  ঘ

  0, π⁄2
• Find the point c in the curve f(x) = x3 + x2 + x + 1 in the interval where slope of a tangent to a curve is equals to the slope of a line joining (0,1)
  ক

  where slope of a tangent to a curve is equals to the slope of a line joining (0,1) ] 0.64

  খ

  0, 1

  গ

  0, 1

  ঘ

  0, 1
• Mean Value theorem is also known as
  ক

  Rolle’s Theorem

  খ

  Lagrange’s Theorem

  গ

  Taylor Expansion

  ঘ

  Leibnitz’s Theorem
• Mean Value theorem is applicable to the and continuous in open interval (a, b) b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) d) Functions differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’
  ক

  Functions differentiable in closed interval and continuous in open interval (a,

  খ

  a, b

  গ

  a, b

  ঘ

  a, b
• If f(
  ক

  is euquals to f( Lebniz Theorem

  খ

  in Mean Value Theorem, then it becomes a) Lebniz Theorem [ Rolle’s Theorem

  গ

  Taylor Series of a function

  ঘ

  Leibnit’x Theorem
• Mean Value Theorem tells about the
  ক

  Existence of point c in a curve where slope of a tangent to curve is equal to the slope of line joining two points in which curve is continuous and differentiable

  খ

  Existence of point c in a curve where slope of a tangent to curve is equal to zero

  গ

  Existence of point c in a curve where curve meets y axis

  ঘ

  Existence of point c in a curve where curve meets x axis
• What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x3 + 5x + 1016 has at least one Rolles point
  ক

  π⁄180 tan-1(5)

  খ

  tan-1(5)

  গ

  180⁄π tan-1(5)
• For the function f(x) = x2 – 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes?
  ক

  3⁄2

  খ

  1⁄2

  গ

  5⁄2