Question

Find tangent line at x=\pi , given: y=3sin^(2 )((x)/(2))

Answer 1

The slope of the tangent line to $y=3\sin^2\dfrac x2$ is

$y'(x)=3\sin\dfrac x2\cos\dfrac x2=\dfrac32\sin x\implies y'(\pi)=0$

which means the tangent line at this point is horizontal.

Because the tangent line passes through

$y(\pi)=3\sin^2\dfrac\pi2=3$

the tangent line has equation $y=3$.