Question

An object moves along the x-axis, its position at each time t being given by x(t). Determine the times from t=0 to t=2pi when the object is moving to the right with increasing speed.

Answer 1

x(t)=sin(t)+cos(t)

Answer 2

x'(t) = cos(t) - sin(t)
Since the thing is increasing speed, x'(t) > 0
cos(t) > sin(t)
Draw out graphs of x = sin t and x = cos t and see what part of cos(t) is > sin(t)