IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

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Consider the function g(x)= rac{1}{a-x} + rac{1}{b-x}

$displaystylelim_{x o a^+}g(x) = - infty$

$displaystylelim_{x o b^-}g(x) = + infty$

Also , g(x) is continuous in (a,b) .

So g(x) takes all the values from ( - infty , infty )

.

So for some x= c in (a,b)

, the curves , f'(x) and g(x) intersect . So f'(c) = g(c)

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