Consider the function y = sin x + x . Calculate the exact value(s) of x for which the slope of the tangent is the steepest on the interval 0 ≤ x ≤ 2π

Answer 1

y= sinx +x

take the derivative:

y' = cosx +1 = the slope of the tangent line

it's steepest when cosx = 1, then the slope =1+1=2= maximum slope

cosx=1

x= cos^-1(1) = 0, 2pi, 2pin where n= any integer

x= 0 or 2pi for the interval [0,2pi]