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(A) Given that $f(x)$ is a differentiable function on $[2, 6]$ and $f^{\prime}(x) \geq 5$ for all $x \in [2, 6]$.By the Mean Value Theorem,for any $x_

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$= 24$

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(A) Given that $f(x)$ is a differentiable function on $[2, 6]$ and $f^{\prime}(x) \geq 5$ for all $x \in [2, 6]$.By the Mean Value Theorem,for any $x_1, x_2 \in [2, 6]$ with $x_2 > x_1$,there exists $c \in (x_1, x_2)$ such that $f^{\prime}(c) = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$.Since $f^{\prime}(x) \geq 5$,we have $\frac{f(6) - f(2)}{6 - 2} \geq 5$.Substituting the value $f(2) = 4$:$\frac{f(6) - 4}{4} \geq 5$$f(6) - 4 \geq 20$$f(6) \geq 24$.Thus,a possible value for $f(6)$ is $24$.

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

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