Where is x^3 + 12x + 5 increasing and decreasing

[teng125]

Find intervals on which f(x)=-x^3 + 12x +5 , -3<x<3 is increasing and decreasing. Where does the function assume extreme values and what are these values ?

does anybody knows how to do this??

 

[TD]

I have the feeling derivatives may be a good idea

Do you know a necessary and/or sufficient condition for extrema, using derivatives?

 

[teng125]

no,pls explain to me

 

[TD]

When a function becomes extreme in a point, the tangent line will be horizontal there which means that the derivative of the function is 0 there. Note that this is a one-way argument, an extremum implies a zero derivative but not the other way arround, so this is a necessary condition - though not sufficient.

To check whether it is actually a min or max, you can use the second derivative or investigate whether the function switches from increasing to decreasing or vice versa arround that point.