Question

identify any maximum or minimum values on the interval $-2leq xleq3$.

1. $f(x)=5x - 2$
2. $f(x)=-2x - 4$

Explanation:

Step1: Analyze the function \(f(x)=5x - 2\)

The function \(y = 5x-2\) is a linear function with slope \(m = 5>0\). A linear function with positive slope is increasing.
On the interval \(-2\leq x\leq3\):
When \(x=-2\), \(f(-2)=5\times(-2)-2=-10 - 2=-12\)
When \(x = 3\), \(f(3)=5\times3-2=15 - 2 = 13\)

Step2: Analyze the function \(f(x)=-2x - 4\)

The function \(y=-2x - 4\) is a linear function with slope \(m=-2<0\). A linear function with negative slope is decreasing.
On the interval \(-2\leq x\leq3\):
When \(x=-2\), \(f(-2)=-2\times(-2)-4=4 - 4=0\)
When \(x = 3\), \(f(3)=-2\times3-4=-6 - 4=-10\)

Answer:

For \(f(x)=5x - 2\): Minimum value is \(-12\) (at \(x = - 2\)) and maximum value is \(13\) (at \(x = 3\)).
For \(f(x)=-2x - 4\): Maximum value is \(0\) (at \(x=-2\)) and minimum value is \(-10\) (at \(x = 3\)).