3.5 Question 197

[Eigenvalue]

Find all x values in the graph of f(x)=-3sin(x)cos(x) where the tangent line is horizontal

[Eigenvalue]

Horizontal tangent line[tex]\rightarrow[/tex] the derivative is 0

f'(x)=-3((sin(x))'cos(x)+sin(x)(cos(x))')
=-3(cos²(x)-sin²(x))
=-3cos(2x)

-3cos(2x)=0
cos(2x)=0

x=[tex]\frac{nπ}{2}[/tex], where n is odd

[nycmath]

Horizontal tangent line[tex]\rightarrow[/tex] the derivative is 0

f'(x)=-3((sin(x))'cos(x)+sin(x)(cos(x))')
=-3(cos²(x)-sin²(x))
=-3cos(2x)

-3cos(2x)=0
cos(2x)=0

x=[tex]\frac{nπ}{2}[/tex], where n is odd

I wish that you would stay focused on Sullivan.