What are the Critical Numbers for f(x) = 2x^3 + 15x^2 - 36x +1?

[ziddy83]

Hi,
i was wondering if anyone could help me.
The problem says find the critical numbers of f...
f(x) = 2x^3 + 15x^2 - 36x +1

ok i found f ' ...6x^2 + 30x-36,
Now how do i start on finding the critical numbers? Do i have to take the second derivative?

 

[Tide]

What, exactly, is the definition of "critical number?" :-)

 

[da_willem]

Definition of a Critical Number

Let f be defined at c. If f'(c) = 0 or f' is undefined at c, then c is a critical number of f.

So should you take a second derivative?

 

[ziddy83]

Right...its not, so I can just set it equal to zero, and then solve for the variable, right?

 

[dextercioby]

Right...its not, so I can just set it equal to zero, and then solve for the variable, right?

Yes,your 'critical numbers' are solution of the equation
$$f'(x)=0$$
.BTW,your terminology is pretty weird.I use to call them "critical points",coz they pop up whenever i want to draw the graph of a function

Daniel.

 

[HallsofIvy]

"Right...its not, so I can just set it equal to zero, and then solve for the variable, right?"

Having determined first that there are no values of x for which the derivative does not exist, yes.

"BTW,your terminology is pretty weird.I use to call them "critical points",coz they pop up whenever i want to draw the graph of a function"

Actually, there is a difference. Given y= f(x), the "critical numbers" are the values of x at which f ' (x) does not exist or is equal to 0. The "critical points" are the points (x,y) with x a critical number.