Mean Value Theorem Application

Mark

The function $f$ is defined by $f(x) = 3x - 4\cos(2x + 1)$ , and its derivative is $f'(x) = 3 + 8\sin(2x + 1)$ . What are all values of $x$ that satisfy the conclusion of the Mean Value Theorem for the function $f$ on the interval $[-1, 2]$ ?

$0.517$

$1.578$

$-0.692$ and $1.263$

$-0.479$ and $1.049$

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