MHB What Are the Absolute Max/Min of f(x) Over Given Intervals?

[riri]

Hello, I'm doing:
Find absolute min/max of f(x)=x^3-12x^2-27x+8

First I found derivative and when I solved, I got x=9 and x=-1.
So I have to find max/min for 3 different intervals:

a) [-2,0]
And I thought absolute max=-1 and absolute min = none?

b) [1,10]
max= none
min= none

c) [-2,10]
max=-1?
min=none again because for x=9, it goes decrease and decrease so it's not min or max.

But NONE of these are right, can anyone help me what I am doing wrong and what they are asking for then?
thank you!

 

[Greg]

$$f'(x)=3x^2-24x-27=3(x+1)(x-9)=0$$
so there is local extremum at $x=-1$ and $x=9$. Plug these values into $f(x)$ to find the values of the extremum. As $f(x)$ tends to $\pm\infty$ as $x$ increases/decreases without bound, there are no defined absolute minimum and absolute maximum.

 

[Prove It]

Hello, I'm doing:
Find absolute min/max of f(x)=x^3-12x^2-27x+8

First I found derivative and when I solved, I got x=9 and x=-1.
So I have to find max/min for 3 different intervals:

a) [-2,0]
And I thought absolute max=-1 and absolute min = none?

b) [1,10]
max= none
min= none

c) [-2,10]
max=-1?
min=none again because for x=9, it goes decrease and decrease so it's not min or max.

But NONE of these are right, can anyone help me what I am doing wrong and what they are asking for then?
thank you!

The absolute maximum or absolute minimum of a function over an interval can occur either at a turning point or an end point.

Also the maximum/minimum VALUE of the function is the y value, positioned where x = blah...

- - - Updated - - -

$$f'(x)=3x^2-24x-27=3(x+1)(x-9)=0$$
so there is local extremum at $x=-1$ and $x=9$. Plug these values into $f(x)$ to find the values of the extremum. As $f(x)$ tends to $\pm\infty$ as $x$ increases/decreases without bound, there are no defined absolute minimum and absolute maximum.

Except that the OP needs to find the absolute max/min of the function IN THE INTERVALS PROVIDED.

 

[offirgo]

Hello, I'm doing:
Find absolute min/max of f(x)=x^3-12x^2-27x+8

First I found derivative and when I solved, I got x=9 and x=-1.
So I have to find max/min for 3 different intervals:

a) [-2,0]
And I thought absolute max=-1 and absolute min = none?

b) [1,10]
max= none
min= none

c) [-2,10]
max=-1?
min=none again because for x=9, it goes decrease and decrease so it's not min or max.

But NONE of these are right, can anyone help me what I am doing wrong and what they are asking for then?
thank you!

check this out and let me know if you have further questions, I am here to help