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Which of the functions in Exercises $7-12$ satisfy the hypotheses of the Mean Value Theorem on the given interval, and which do not? Give reasons for your answers.$$f(x)=\left\{\begin{array}{ll}{x^{2}-x,} & {-2 \leq x \leq-1} \\ {2 x^{2}-3 x-3,} & {-1 < x \leq 0}\end{array}\right.$$
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Calculus 1 / AB
Chapter 4
Applications of Derivatives
Section 2
The Mean Value Theorem
Applications of the Derivative
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and this problem, we're given a function and where f changes very mingle the, uh the offense and we want to get the military is applicable for dysfunction. Boerner. In order for me, Millie, terms be applicable. We want function to be continuous in the Iranian Terrible, um, negative to zero. You want it to be differential in the opening to relate to. To hear let's check for continue what's related function actually at the auto point. So let's look at estimating it's one. So we have negative one. If you pardon. It's one of the, uh, argument. Top native one scrape minus one. But we planned this to be, too. And let's do the same or the bottom Well to tell Deputy will spread my seat, Tenzing one like street. And again we find this to be too. So s I chilies looking. So analysis Check boarding virtuality. Let's Wendy, they would talk about Parma. Becks is to explain one and eternal negative too, and then into one. And it is old X minus three internal negative one and zero. Again, let's check the derivative at T out of port. So too takes excellent 12 time thing is one minus 14 times Like I want my street sometimes irritable my swim. We want this to be negative. Three second we but meaning someone seems those are not equal We can set up. Is that differential? So since epicenter perishable, This is not satisfied. So mean Mellet does not it?
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