Question

Is the graph of y=sin(x^6) increasing or decreasing when x=12

Answer 1

The rate of change, i.e. slope of
y=sin(x^6)
is
y'=dy/dx=cos(x^6)*(6x^5)

Substitute x=12 (radians)
y'(12)=cos(12^6)*(6*12^5)
=1492992cos(2985984)
=1128592.5 >0

Therefore y(x) is increasing at x=12 (radians).