Question

# According to LMVT, if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then which of the following option should be correct for some value c from the interval (a,b)?( c can take any value from the interval (a,b) )

A

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B

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C

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D

None of the above

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Solution

## The correct option is B LMVT theorem states that if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then we’ll have slope of the tangent drawn at some x = c where c ∈ (a, b) equal to the slope of secant joining points (a, f(a)) & (b, f(b)). Slope of tangent at x =c is f’(c). Slope of secant is the average rate of change of f(x) over the interval [a,b] ⇒f′(C)=f(a)−f(b)a−b

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