Question

HELP!!!!! I dont understand this!​

Answer 1

-14

Explanation:

I might be wrong, but this is my interpretation of the problem.

To solve this problem, find the endpoints of the line in the interval. Then draw a line between those two points. Finally, find the slope of the line that passes between the two points.

The line is f(x) = -2x^(2) + 2x + 1

The interval (in standard notation) is (3
`\leq` x
`\leq` 5)

So when x = 3,

-2x^(2) + 2x + 1

-2(3)^(2) + 2*3 + 1

-2 * 9 + 6 + 1

-18 + 7

- 11

One endpoint is: (3, -11).

When x = 5

-2x^(2) + 2x + 1

-2(5)^2 + 2*5 + 1

-2 * 25 + 10 + 1

-50 + 11

-39

The other endpoint is; (5, -39).

Find the slope of a line passing through these two points.

The formula to find the slope of a line is:

`(y_(2) - y_(1) )/(x_(2) - x_(1) )`

`x_(1)` = 3

`y_(1)` = -11

`x_(2)` = 5

`y_(2)` = -39

((-39) - ( -11))/((5) - (3))

Simplify

-28/2

-14