Consider the differentiable function on the closed interval .What is the value of in the interval that satisfies the Mean Value Theorem? Round your answer to 3 decimal places.

Question

​Consider the differentiable function  on the closed interval  .What is the value of  in the interval  that satisfies the Mean Value Theorem? Round your answer to 3 decimal places. ​

Quizplus · Accepted Answer

By the Mean Value Theorem, there exists a value c in [−2, 2] such that f′(c)=f(2)−f(−2)4. Evaluating f(2)−f(−2)4 gives (7−1)4=32. Since f′(x)=3x2−2, we need to solve 3c2−2=32. This gives c=±√34. Since √34 is within the interval [−2,2], we take c=√34. Evaluating f(√34) gives approximately 1.785. Rounded to 3 decimal places, the answer is 1.785.

​Consider the Differentiable Function on the Closed Interval

Consider the Differentiable Function on the Closed Interval