Asked by Sara

Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π]
Answered by Sara
i found the derivative to be y'=2cosx but i don't know what to do next
Answered by Steve
well, where is cosx a maximum? At x=0.
So, at x=0, the slope of 2sinx = 2.
2sin(0) = 0, so, at (0,0) the slope is 2.

The line is y=2x.

By now you should know that sin(x) has its maximum slope where it crosses the x-axis. That's what we have calculated here.
Answered by Sara
how is the slope of 2sinx=2?
Answered by Sara
because f'(0)=2cos(0)=2?
Answered by Sara
also, how is y=2x? did you use y=mx+b? which numbers did you substitute?
Answered by Damon
he said at (0,0) the slope is 2
That is a line through the origin with slope = 2
y = 2 x + 0