Question

find the absolute and local maximum and minimum values of f.f(x) = 8 - 2x
x ≥ 1

Answer 1

Is this calculus? Or algebra 2?

Answer 2

Find all critical points and plug them in to the function and the highest number is the absolute max and lowest is the absolute min.

Dont forget to include 1 since that's one bound.

Answer 3

how do i find the criteria

Answer 4

Are you taking algebra, or calculus?

Answer 5

Because there are a few ways to do this depending on what you know.

Answer 6

calculus

Answer 7

Ok, so take the derivative of f. What do you have?

Answer 8

-2

Answer 9

Right. So when you are finding local mins/maxes you are looking for places where the derivative is 0. When is -2=0?

Answer 10

never lol

Answer 11

So there are no local mins or maxes. So you just have to look at the value at the "end" points for absolute mins/maxes. Which is to say x=1, there is no other end point because the other bound goes to \(\infty\)

Answer 12

So what is the value at x=1?

Answer 13

6

Answer 14

And what happens as x gets larger? Is f(1)=6 an absolute min or is it a max?

Answer 15

max

Answer 16

so 6 is the max

Answer 17

Yes. And it has no absolute min, and no local mins or maxes.

Answer 18

ok i get it!!!

Answer 19

thank u!

Answer 20

Of course!