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$If c is a point at which Rolle's theorem holds for the function, f (x) = \log_{e} (\frac{x^{2} + α}{7 x}) in$
$the interval [3, 4], where α \in R, then f^{''} (c) is equal to:$

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detailed solution

Correct option is D

f(3)=f(4)⇒α=12 f'(x)=x2-12xx2+12∴ f'(c)=0∴ c=12∴ f''(c)=112

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If c is a point at which Rolle's theorem holds for the function, f(x)=logex2+α7x in the interval [3,4], where α∈R, then f''(c) is equal to:

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Ready to Test Your Skills?

free study material

$If c is a point at which Rolle's theorem holds for the function, f (x) = \log_{e} (\frac{x^{2} + α}{7 x}) in$
$the interval [3, 4], where α \in R, then f^{''} (c) is equal to:$