Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π]

Question

I believe the equation is y=2x-4pi. How is the b-value -4pi?

Answer 1

y' = 2cosx
y" = -2sinx

y' is max when y" = 0, at 0,π,2π
y'(π) = -2
y'(2π) = 2

So, the point (2π,0) has max slope.

y = 2(x-2π)

Note that x=0 is not in the given domain.

b is clearly not 4π

See the graphs at

http://www.wolframalpha.com/input/?i=plot+y%3D2sinx%2C+y%3D2x%2C+y%3D2x-4%CF%80