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5. Continuity and Differentiation
hard
ધારો કે વિધેય $f$ એ $[\mathrm{a}, \mathrm{b}]$ પર સતત અને $(a, b) $ પર દ્રીતીય વિકલનીય છે. જો દરેક $x \in(a, b)$ ; $f^{\prime}(\mathrm{x})>0$ અને $f^{\prime \prime}(\mathrm{x})<0,$ હોય તો કોઈક $\mathrm{c} \in(\mathrm{a}, \mathrm{b})$ ; $\frac{f(\mathrm{c})-f(\mathrm{a})}{f(\mathrm{b})-f(\mathrm{c})}$ $>$
A
$\frac{b+a}{b-a}$
B
$\frac{b-c}{c-a}$
C
$\frac{c-a}{b-c}$
D
$1$
(JEE MAIN-2020)
Solution
it is clear from graph that $\mathrm{m}_{1}>\mathrm{m}_{2}$
$\Rightarrow \quad \frac{f(\mathrm{c})-f(\mathrm{a})}{\mathrm{c}-\mathrm{a}}>\frac{f(\mathrm{b})-f(\mathrm{c})}{\mathrm{b}-\mathrm{c}}$
$\Rightarrow \quad \frac{f(c)-f(a)}{f(b)-f(c)}>\frac{c-a}{b-c}$
Standard 12
Mathematics
