Math  /  Calculus

QuestionSelected values of the function ff are shown in the table below. The function ff is continuous on the closed interval [3,2][-3,2] and differentiable on the open interval (3,2)(-3,2). Determine the validity of the following statement:
There exists a value cc in the open interval (3,2)(-3,2) such that f(c)=6f^{\prime}(c)=6. \begin{tabular}{|c|c|} \hlinexx & f(x)f(x) \\ \hline-3 & -9 \\ \hline-1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular}
Answer the statement must be true Submit Answer the statement must be false the statement could be either true or false

Studdy Solution
The MVT guarantees that there exists some c c in (3,2)(-3, 2) such that f(c)=2.6 f^{\prime}(c) = 2.6 .
Since f(c)=6 f^{\prime}(c) = 6 is not equal to the value 2.6 2.6 guaranteed by the MVT, the statement that f(c)=6 f^{\prime}(c) = 6 must be false.
The statement must be false.

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