Question

find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x - values at which they occur.
$f(x)=5x - 9$
(a) $0,3$
(b) $-2,4$
(a) the absolute maximum value is $\square$ at $x = \square$
(use a comma to separate answers as needed.)

Explanation:

Step1: Find the derivative of the function

The function is \(f(x) = 5x-9\). The derivative \(f^\prime(x)=\frac{d}{dx}(5x - 9)=5\). Since \(f^\prime(x)=5>0\) for all \(x\), the function \(y = f(x)\) is increasing on the entire real - line.

Step2: Evaluate the function at the endpoints of the interval \([0,3]\)

For \(x = 0\):
\(f(0)=5\times0 - 9=-9\)
For \(x = 3\):
\(f(3)=5\times3-9=15 - 9 = 6\)

Answer:

The absolute maximum value is \(6\) at \(x = 3\).