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 )equals8 x minus 5 ​(A) ​[0​,4​] ​ (B) [negative 4 comma 3 ]

Answer 1

a. Maximum= 27, minimum= -5

b. Maximum= 19, minimum=-37

Explanation:

We have the function
`f(x)=8x-5`. Since the function correspond to a line, then the maximum and minimum values of the function over an interval are in the endpoints of the interval.

Observe that if the line has negative slope then the minimum value is in the right endpoint. If the line has positive slope the minimum value is in the left endpoint of the interval.

The function f(x) has slope m=8. Then

a. the minimum value of f(x) in the interval [0,4] is reach when x=0, and the minimum is
`f(0)=8*0-5=-5` and the maximum is
`f(4)=8(4)-5=32-5=27`

b. the minimum value of f(x) in the interval [-4,,3] is reach when x=-4, and the minimum is
`f(-4)=8(-4)-5=-32-5=-37` and the maximum is
`f(3)=8(3)-5=24-5=19`