Question

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(f(8) = 64).

the intermediate value theorem guarantees a solution to (f(x) = 37) in the interval ((0,8)) because

(f(\quad) \le \quad \le f(\quad)).

Explanation:

Step1: Identify interval endpoints

The interval is \((0,8)\), so the endpoints are \(x = 0\) and \(x = 8\).

Step2: Find endpoint values

From the graph, \(f(0) = 0\) and \(f(8) = 64\).

Step3: Apply IVT inequality

Since \(0 \le 37 \le 64\), we write \(f(0) \le 37 \le f(8)\).

Answer:

\(f(0) \le 37 \le f(8)\)