Question

Without sketching the graph of the function, find the maximum value of y = - 5x + 4 over the interval - 4 <= x <= 3. Explain how you found this value.

Answer 1

`y_(max)=24`

Explanation:

Given function
`y=-5x+4` is linear function. This linear function represents the straight line on the coordinate plane. The slope of this line is
`-5.` Since the slope is negative, the linear function is decreasing for all x. This means

`\text{ if } x_1<x_2, \text{ then } f(x_1)> f(x_2)`

You ar geven the interval
`-4\le x\le 3.` So, the maximum value of the function is at the point x=-4 and the minimum value of the function is at the point x=3.

At x=-4,

`y=-5\cdot (-4)+4=20+4=24.`