In a word, no.
But it’s a great question with a really interesting answer. If you ever have a student in your calculus class ask this question, then you are doing something very right.
But let’s take a step back. What does the title of this post even mean? As discussed in my last post, the MVT states that f’ (if it exists on a closed interval) must equal its average value somewhere in that interval. And it is clearly true (thanks to the IVT) that any continuous function equals its average value at some point in a closed interval. This suggests that we can easily prove the MVT by invoking the IVT. The “proof” goes like this:
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