Question

for the graph of f(x) = x^3 - 3x + 1
[0,3], how would i work out the absolute maximum?

Answer 1

this is the graph and i can tell that the absolute minimum is -1

Answer 2

https://www.khanacademy.org/math/differential-calculus/derivative_applications/critical_points_graphing/v/identifying-minima-and-maxima-for-x-3-12x-5

this video will definitely help you :)
@swift_13

Answer 3

my internet is going super slow at the moment, can you please explain it?

Answer 4

take the derivative of your function

Answer 5

3x-3

Answer 6

than?

Answer 7

solve for your critical points, then sub those values and your endpoints into the original function. The highest value of y is your absolute maximum

Answer 8

3x^2 -3

Answer 9

now solve for zero

Answer 10

take those zeros, plus 0 and 3 and sub back into f(x)

Answer 11

taking zero x=-1 or 1

Answer 12

good..then put the values of x(1 or -1) in your equation,then the maximum value you got,is the ABSOLUTE MAXIMUM and minimum value you got is ABSOLUTE MINIMUM.

Answer 13

understood? @swift_13

Answer 14

don't forget the endpoints

Answer 15

and the end points mean its VERTEX

Answer 16

so putting -1 or 1 in f(x) gives me 1

Answer 17

if this is calculus and I am assuming you are in calculus. The absolute maximum is the highest point

Answer 18

from the graph, it is clear that the `absolute maximum` in given interval occurs at `x = 3`.
so you can simply evaluate f(3)

Answer 19

f(-1)
f(1)
f(0)
f(3)

Answer 20

-1 is not a part of the given domain

Answer 21

you may use calculus for finding absolute minimum though

Answer 22

true so you don't do f(-1) since you evaluate from (0,3)

Answer 23

technically [0,3]

Answer 24

ohk

Answer 25

f(1)=1
f(0)=1
f(3)=19

Answer 26

`f(1)=-1`

Answer 27

when you have a graph, you should stare at it and think a bit on what was being asked to find out before rushing to solve

Answer 28

but absoulte minimum is ment to be -1

Answer 29

ok absolute min at f(1)=-1 and absolute max at f(3)=19