3.5 Question 198

[Eigenvalue]

Find all x values on the graph of f(x)=x-2cos(x) for 0<x<2π where the tangent line has slope 2

[nycmath]

Perhaps you can show us.

[Eigenvalue]

Tangent line with slope 2[tex]\rightarrow[/tex] derivative of 2
f(x)=x-2cos(x)
f'(x)=1-2(-sin(x))=1+2sin(x)

1+2sin(x)=2
sin(x)=[tex]\frac{1}{2}[/tex]

x=[tex]\frac{π}{6}[/tex] or x=[tex]\frac{5π}{6}[/tex]

[nycmath]

Tangent line with slope 2[tex]\rightarrow[/tex] derivative of 2
f(x)=x-2cos(x)
f'(x)=1-2(-sin(x))=1+2sin(x)

1+2sin(x)=2
sin(x)=[tex]\frac{1}{2}[/tex]

x=[tex]\frac{π}{6}[/tex] or x=[tex]\frac{5π}{6}[/tex]

Wish I knew what all of this means. In 2027, I will know.