Question

Consider the linear function f(x)=mx+b, where m ≠0, on the interval [3,7]. Explain why the maximum value of the function over this interval must occur at one of the endpoints of the interval.

Please Explain it’ll be greatly appreciated!! Thank you in advance!!

Answer 1

the function is either increasing or decreasing

Explanation:

For m ≠ 0, the function must be either increasing or decreasing. If the function is increasing, it will have its maximum value at the right end of the interval. If it is decreasing, its maximum value will be at the left end of the interval.