A function y=f(x) with f(-1)=-249 has no maxi | vedclass

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(A) Given that $f(x)$ has a minimum at $x=5$ with $f(5)=75$. If $f(x)$ were continuous on the interval $[-1, 5]$, then by the Extreme Value Theorem, i

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At some point in $(-1,5)$, $f(x)$ is discontinuous

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(A) Given that $f(x)$ has a minimum at $x=5$ with $f(5)=75$. If $f(x)$ were continuous on the interval $[-1, 5]$, then by the Extreme Value Theorem, it must attain a maximum and a minimum on this closed interval. Since $f(-1) = -249$ and $f(5) = 75$, if the function were continuous, there would exist some $c \in (-1, 5)$ such that $f(c)$ is a local maximum or the function would have to increase from $-249$ to $75$. However, the problem states that the function has no maximum and only one minimum at $x=5$. If $f(x)$ were continuous, it would contradict the given conditions because a continuous function on a closed interval must have a maximum. Therefore, $f(x)$ must be discontinuous at some point in the interval $(-1, 5)$ to avoid having a maximum.

$A$ function $y=f(x)$ with $f(-1)=-249$ has no maximum and has only one minimum at $x=5$ with $f(5)=75$. Which one of the following is true?

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