3.5 Question 199

[Eigenvalue]

Let f(x)=cot(x). Detrrm the points on the graph where the tangent line(s) is (are) parallel to y=-2x

[nycmath]

Why don't you show us?

[Eigenvalue]

Parallel to y=-2x[tex]\rightarrow[/tex] derivative of -2

f(x)=cot(x)
f'(x)=-csc²(x)

-csc²(x)=-2
csc²(x)=2
sin²(x)=[tex]\frac{1}{2}[/tex]
sin(x)=±[tex]\frac{ \sqrt{2} }{2}[/tex]

x=[tex]\frac{π}{4}[/tex], [tex]\frac{3π}{4}[/tex], [tex]\frac{5π}{4}[/tex], [tex]\frac{7π}{4}[/tex]

[nycmath]

Parallel to y=-2x[tex]\rightarrow[/tex] derivative of -2

f(x)=cot(x)
f'(x)=-csc²(x)

-csc²(x)=-2
csc²(x)=2
sin²(x)=[tex]\frac{1}{2}[/tex]
sin(x)=±[tex]\frac{ \sqrt{2} }{2}[/tex]

x=[tex]\frac{π}{4}[/tex], [tex]\frac{3π}{4}[/tex], [tex]\frac{5π}{4}[/tex], [tex]\frac{7π}{4}[/tex]

Round and round and round she goes. Where she stops only math people know.