To find the absolute maximum and minimum of the function f(x) = x + ln(x) on [0.5, 8], one must calculate the derivative, identify critical points, and evaluate the function at these points and interval endpoints. The actual maximum and minimum values cannot be provided without further calculations.
The student is asking to find the absolute maximum and minimum values of the function f(x) = x + ln(x) on the interval [0.5, 8]. To find these values, one would typically calculate the derivative of the function, set it equal to zero to find critical points, and then evaluate the function at these points and at the endpoints of the given interval.
The points where the function has the highest and lowest values will be the absolute maximum and minimum, respectively. However, without the actual function and derivative calculations provided, this answer is a generic approach and does not provide the exact maximum and minimum values for the function.
The graph of f(x) = x + ln(x) will generally rise as x increases since both x and ln(x) are increasing functions. In the given interval, the natural logarithm is defined and the function is continuous, so the absolute maximum and minimum must occur either at critical points or at the endpoints of the interval.