If $f(x)$ is a differentiable function, $f^{\prime}(x) \geq 5 \forall x \in[2,6]$, $f(2)=4$ and $f(3)=15$, then a possible value of $f(6)$

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Aicharya · Accepted Answer

Since $f(3) 
eq f(2)$ $	herefore$ Using Mean value theorem $ \begin{aligned} & f^{\prime}(x)=\frac{f(3)-f(2)}{3-2}=\frac{15-4}{3-2} \ & \Rightarrow f^{\prime}(x)=11 \ & \Rightarrow f^{\prime}(x) \geq 5 \ & \Rightarrow \frac{f(6)-f(2)}{6-2} \geq 5 \ & \Rightarrow f(6)-4 \geq 20 \ & \Rightarrow f(6) \geq 24 \ & \Rightarrow 	ext { Possible values of } f(6)=24 . \end{aligned} $

If $f(x)$ is a differentiable function, $f^{\prime}(x) \geq 5 \forall x \in[2,6]$, $f(2)=4$ and $f(3)=15$,…

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