Question

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.
f(x)=6x + 7
(a)0,9 (b)-2,6
(a) the absolute maximum value is at x =.
(use a comma to separate answers as needed.)

Explanation:

Step1: Analyze the function's derivative

The function \(f(x) = 6x + 7\). The derivative \(f^\prime(x)=6\). Since \(f^\prime(x)>0\) for all \(x\), the function is increasing on \((-\infty,\infty)\).

Step2: Evaluate the function at the endpoints of the interval \([0,9]\)

For \(x = 0\):
\(f(0)=6\times0 + 7=7\)
For \(x = 9\):
\(f(9)=6\times9+7=54 + 7=61\)

Answer:

The absolute maximum value is \(61\) at \(x = 9\).