Question

Find the global maximum and minimum for the function on the closed interval.

f(x)=x^3 - 3x^2 + 2
1≤x≤3

Write the x values in increasing order.

The global minimum at x=_____ and x=____ is _____.

The global maximum at x=_____ and x=____ is _____.

please explain! thank you:)

Answer 1

find all the local max/mins first

Answer 2

i do not by finding the derivatives first right?

f ' (x)= 3x^2 - 6x

and f '' (x)= 6x-6

?

Answer 3

yes, the slope is 0 at max/min points

Answer 4

so set the first derivative to 0
and solve x

Answer 5

f ' (x)= 3x^2 - 6x = 0

x = ?

Answer 6

okay

so

3x(x-6)=0

x=0; x=6 ?

Answer 7

yes, 0 and 6 are the critical points

Answer 8

u familiar wid second derivative test ?

Answer 9

it is not needed for doing this problem,
but if you're familiar wid that, we can use it...

Answer 10

is it where you use the signs? like this?