The table gives selected values of the continuous function $$g$$. ![](http://admin.getprephub.com/media/editor/af6_20221017233844980392.png) Can we use the mean value theorem to say the equation $$g^{\prime}(x)=\frac{1}{2}$$ has a solution where $$100<x<101$$ ?

First the function has to be differentiable to be applied by Mean Value theorm So, No, since, we do not know if the function is differentiable.

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The table gives selected values of the continuous function $g$ .

Can we use the mean value theorem to say the equation $g^{\prime}(x)=\frac{1}{2}$ has a solution where $100<x<101$ ?

Select all that apply :

No, since we do not know if the function is differentiable on that interval.

No, since the average rate of change of $g$ over the interval $100 \leq x \leq 101$ isn’t equal to $\frac{1}{2}$ .

Yes, both conditions for using the mean value theorem have been met.

None of the above

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