Question

and we check the value of (f) at the right endpoint of the interval (0,8):

(f(8) = 64).

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

Explanation:

Step1: Identify the function type

The graph shows a parabola passing through the origin \((0,0)\) and \((2,0)\).

$$f(x) = ax(x-2)$$

Step2: Determine the coefficient

Using the point \((8, f(8))\) and the horizontal line representing \(y = 37\), we find the scale factor \(a = 1\).

$$f(x) = x(x-2)$$

Step3: Calculate the value

Substitute \(x = 8\) into the function.

$$f(8) = 8(8-2) = 48$$

Answer:

\(f(8) = 48\)