Question

Find the values of x on the interval [0, π] where the tangent line to the graph of y = sin(x) cos(x) is horizontal. (Enter your answers as a comma-separated list.)

Answer 1

y = sinxcosx
dy/dx = cos^2x - sin^2x = cos2x

For the tangent to be horizontal, dy/dx = 0 => cos2x = 0
2x = (2n+1)pi/2

x = (2n+1)pi/2

=> x = pi/2 (only possible value since x lies in the interval [0,pi])