Question
Find the value of $c$ in $[- 5, - 2]$ such that $f (c)$ equals the average value of $f (t) = - 6 t - 2$ over the interval $[- 5, - 2]$ . Enter your answer as an exact fraction if necessary.

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Final Answer: $c = - \frac{7}{2}$

Steps

Step 1 ：First, we need to calculate the average value of the function $f (t) = - 6 t - 2$ over the interval $[- 5, - 2]$ . The average value of a function over an interval $[a, b]$ is given by the formula $\frac{1}{b - a} \int_{a}^{b} f (t) d t$ .

Step 2 ：Next, we need to find the value of $c$ in $[- 5, - 2]$ such that $f (c)$ equals this average value. We do this by solving the equation $f (c) = average value$ for $c$ .

Step 3 ：The solution to the equation $f (c) = average value$ is $c = - \frac{7}{2}$ .

Step 4 ：This means that the value of $c$ in $[- 5, - 2]$ such that $f (c)$ equals the average value of $f (t)$ over the interval $[- 5, - 2]$ is $- \frac{7}{2}$ .

Step 5 ：Final Answer: $c = - \frac{7}{2}$

QuestionFind the value of c in [−5,−2] such that f(c) equals the average value of f(t)=−6t−2 over the interval [−5,−2]. Enter your answer as an exact fraction if necessary.

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Question
Find the value of $c$ in $[- 5, - 2]$ such that $f (c)$ equals the average value of $f (t) = - 6 t - 2$ over the interval $[- 5, - 2]$ . Enter your answer as an exact fraction if necessary.