Let $f:[1,3] \rightarrow \mathbb{R}$ be continuous and be derivable in $(1,3)$ and $f^{\prime}(x)=[f(x)]^2+4 \forall x \in(1,3)$. Then

Question

Let $f:[1,3] \rightarrow \mathbb{R}$ be continuous and be derivable in $(1,3)$ and $f^{\prime}(x)=[f(x)]^2+4 \forall x \in(1,3)$. Then, $f(3)-f(1)=5$ holds, $f(3)-f(1)=5$ does not hold, $f(3)-f(1)=3$ holds, $f(3)-f(1)=4$ holds

MARKS App · Accepted Answer

$\begin{aligned} & \text { Hint : } f^{\prime}(c)=(f(c))^2+4=\frac{f(3)-f(1)}{2} \ & \Rightarrow f(3)-f(1)=2(f(c))^2+8 \end{aligned}$

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