Let $f:[1,3] \rightarrow R$ be a continuous function that is differentiable in $(1,3)$ an $f^{\prime}(x)=|f(x)|^{2}+4$ for all $x \in(1,3)$. Then,

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Let $f:[1,3] \rightarrow R$ be a continuous function that is differentiable in $(1,3)$ an $f^{\prime}(x)=|f(x)|^{2}+4$ for all $x \in(1,3)$. Then,

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kritika · Answer 1 · 2021-12-27T04:32:56+0000

Ans : $(B, C)^{*}$
Hint : By applying LMVT, there exist at least one $c \in(1,3)$ such that $\frac{f(3)-f(1)}{3-1}=f^{\prime}(c)$
$$
\Rightarrow \mathrm{f}(3)-\mathrm{f}(1)=2 \cdot|\mathrm{f}(\mathrm{c})|^{2}+8 \Rightarrow \mathrm{f}(3)-\mathrm{f}(1) \geq 8
$$

Let \(f:[1,3] \rightarrow R\) be a continuous function that is differentiable in \((1,3)\) an \(f^{\prime}(x)=|f(x)|^{2}+4\) for all \(x \in(1,3)\). Then,

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