Question

find the values of x between 0 and 2pi where the tangent line to the graph of y=sinxcosx is horizontal.

Answer 1

  y = sin x + cos x 

the tangent will be horizontal when the derivative is 0 

y ' = cos x - sin x 
0 = cos x - sin x 
sin x = cos x 
tan x = 1 
this happens when x = pi/4 or 5pi/4 

y(pi/4) = sqrt(2) / 2 + sqrt(2) / 2 = sqrt(2) 
y(5pi/4) = -sqrt(2) / 2 + -sqrt(2) / 2 = -sqrt(2) 

the two points are: (pi/4 , srqt(2)) and (5pi/4 , -srqt(2))

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