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Let f be any function continuous on

Question:

Let $f$ be any function continuous on $[\mathrm{a}, \mathrm{b}]$ and twice differentiable on (a, b). If for all $x \in(a, b)$, $f^{\prime}(\mathrm{x})>0$ and $f^{\prime \prime}(\mathrm{x})<0$, then for any $\mathrm{c} \in(\mathrm{a}, \mathrm{b})$,

$\frac{f(c)-f(a)}{f(b)-f(c)}$ is greater than :

  1. $\frac{b+a}{b-a}$

  2. $\frac{b-c}{c-a}$

  3. $\frac{c-a}{b-c}$

  4. 1


Correct Option: , 3

Solution:

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