Question

calc question

Answer 1

So first I find the critical numbers is that right?

Answer 2

Yes.

Answer 3

Okay,
f ' (x)= -2x+4
0 = -2x + 4
x= 2 (critical number)

Answer 4

then what ?

Answer 5

0 and 5 are critical numbers as well.

Answer 6

So whenever I am given the interval the end and the begging of the interval will be a critical number?

Answer 7

If it is closed interval.

Answer 8

Okay:)

Answer 9

so the critical numbers are 0,2,5.

Answer 10

What do I do next?

Answer 11

find the values of \(f(x)\) at the critical numbers.

Answer 12

Okay,
f(0)=-x^2+4x+12=12
f(2)=-x^2+4x+12=16
f(5)=-x^2+4x+12=7

Answer 13

The critical number that gives highest value for \(f\) will be the maximum

Answer 14

So, the absolute maximum occurs at x=2, and absolute minimum at x=5 ?

Answer 15

or just the maximum part of my statement is good?

Answer 16

Well, the question answers that question.

Answer 17

the question answers that question? I am sorry, but I don't quite get you-:(

Answer 18

It asks for both minimum and maximum.

Answer 19

So I was right, the abs min is 7, and abs max is 16 ?

Answer 20

yes

Answer 21

And if i am not confusng the abs max and min is the y-value, not a point or an x-value.

Answer 22

*confusing

Answer 23

The max/min will be the output of the function.

Answer 24

Yes. I was just abt to explain what I meant, but you got me:)
Tnx for the help!

Answer 25

bye