Finding horizontal tangents on an interval

[noelwolfe]

Homework Statement

Determine all x in [-pi/2, pi/2] at which the graph has horizontal tangents.

Homework Equations

1.) f'(x)= 9cos(x)-2sin(x)
2.) f'(x)= -5csc(x) (5cot(x)-csc(x))

The Attempt at a Solution

1.) 9cos(x)=2sin(x)
9/2=sin(x)/cos(x)
9/2=tan(x)
and then I'm not sure what to do with 9/2?

2.) 5cot(x)=csc(x)
5= csc(x)/cot(x)
5=1/cos(x)
cos(x)=1/5
same problem here... what do I do with 1/5?

 

[hotvette]

9/2=tan(x)
and then I'm not sure what to do with 9/2?

You are looking for the values of x such that tan(x) = 9/2. Remember inverse trigonometric functions (i.e. sine / arcsine, cos / arccos, tan / arctan, etc.)?

 

[noelwolfe]

I'm sorry, I still don't know--I'm not aware of a "simple" solution to tan(x)=9/2. How would I go about finding the solution?

 

[einsteinoid]

Look up the arctan function (also called inverse tangent) and its uses.

 

[noelwolfe]

Got it. Thanks!