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Solved Examples
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ee  Determine the point on the parabola f (x) = (x - 6)2, at which the tangent is parallel to the chord joining the points (6, 0) & (7, 1).
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ee  We verify the "Mean Value theorem" for a function f (x):
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ee  Which of the following functions satisfies the mean value theorem?  ee View Solution
ee  Determine the point on the parabola f (x) = (x - 7)2, at which the tangent is parallel to the chord joining the points (7, 0) & (8, 1).
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ee  Find the point on the parabola y = (x + 3)2, at which the tangent is parallel to the chord of the parabola joining the points (- 3, 0) & (- 4, 1).   ee View Solution
ee  Find the point on the graph of f (x) = x3, at which the tangent is parallel to the chord joining the points (1, 1) & (3, 27).   ee View Solution
ee  Find the point at which the tangent to the curve f(x) = x2 - 6x + 1 is parallel to the chord joining the points (1, - 4) & (3, -8).  ee View Solution
ee  Find the point on the curve y = 12(x + 1)(x - 2) in the interval [-1, 2], at which the tangent is parallel to the x - axis.  ee View Solution
ee  State whether the function f (x) = 3x2 - 2 on [2, 3] satisfies the mean value theorem.  ee View Solution
ee  State whether the function f(x) = ln x on [1, 2] satisfies the mean value theorem.
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ee  State whether the function f (x) = sin x - sin 2x, x [0, π] satisfies the mean value theorem.
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ee  Find the value of c that satisfies the conclusion of the mean value theorem for f (x) = x3 - 2x2 - x + 3 on [0, 1].
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ee  If f (x) = (x -2) lnx, then there exists at least one value of x in (1, 2) such that x ln x + x =
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ee  Find the value of c that satisfies the conclusion of the mean value theorem for the function f (x) = ln x in [1, e].  ee View Solution
ee  Find the value of c that satisfies the conclusion of the mean value theorem for the function f (x) = ex in [0, 1].
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ee  Find the value of c that satisfies the conclusion of the mean value theorem for the function f (x) = sin x in [0, π].  ee View Solution
ee  Find the value of c that satisfies the conclusion of the mean value theorem for the function f (x) = cos x in [- π2 , π2].  ee View Solution
ee  If the value of c that satisfies the conclusion of the mean value theorem for the function f (x) = tan x in [-π4, π4], then sec2 c =
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ee  Select the statement that explains why the mean value theorem does not apply to the function f (x) = | x | in the interval [-1, 1].
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ee  Select the statement that explains why the mean value theorem does not apply to the function f (x) = tan x in the interval [0, π].  ee View Solution
ee  Select the statement that explains why the mean value theorem does not apply to the function f (x) = e1x in the interval [-1, 1].
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ee  If f (x) = e-1x for x [-1, 0) (0, 1] and
           = 1 for x = 0 , then
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ee  Which statement explains why the mean value theorem does not apply to the function f (x) = |x|x in the interval [-2, 2]?  ee View Solution
ee  Every function f (x) that follows the hypotheses of the mean value theorem in [a, b] is  ee View Solution
ee  Identify the condition necessary for a function f (x) to satisfy the mean value theorem in the closed interval [a, b].  ee View Solution
ee  If y = f (x) is a continuous curve from the point A (a, f (a)) to the point B (b, f (b)) which has unique tangent at every intermediate point between A and B, then
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