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By Lagrange’s mean value theorem which of the following statement is true:
(a) If a curve has a tangent at each of its points then there exists at least one-point C on this curve, the tangent at which is parallel to chord AB
(b) If f’(x) = 0 in the interval then f(x) has same value for every value of x in (a, b)
  • a)
    (a) alone is true
  • b)
    (b) alone is true
  • c)
    Both (a) and (b) are true
  • d)
    Neither (a) nor (b) is true
Correct answer is option 'A'. Can you explain this answer?
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By Lagrange’s mean value theorem which of the following statemen...
Concept:
Lagrange’s Mean Value Theorem:
If f(x) is real valued function such that –
  • f(x) is continuous in the closed interval [a,b]
  • (f(x) is differentiable in the open interval (a,b)
  • f(a) ≠ f(b)
Then there exist at least one value x, c (a,b) such that –


Geometrical Interpretation:
  • Between two points a and b, f(a) ≠ f(b) of the graph of f(x) then there exists one point where the tangent is parallel to the chord 
Explanation:
(a) is true with reference to geometrical interpretations.
(b) is false, if f(x) has same value for every value of x, it will violate f(a) ≠ f(b).
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By Lagrange’s mean value theorem which of the following statement is true:(a) If a curve has a tangent at each of its points then there exists at least one-point C on this curve, the tangent at which is parallel to chord AB(b) If f’(x) = 0 in the interval then f(x) has same value for every value of x in (a, b)a)(a) alone is trueb)(b) alone is truec)Both (a) and (b) are trued)Neither (a) nor (b) is trueCorrect answer is option 'A'. Can you explain this answer?
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