Answer:
Step-by-step explanation:
According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one <em>c</em> within (a, b) such that f'(c) = 0.
We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a <em>c</em> in (5, 8) such that g'(c) = 0.
So, differentiate the function. We can take the derivative of both sides with respect to <em>x: </em>
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Differentiate:
Let g'(x) = 0:
Solve for <em>x</em>. First, divide everything by negative seven:
Factor:
<h3>Zero Product Property:
Solve for each case. Hence:
Since the first solution is not within our interval, we can ignore it.
Therefore:
