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\frac x2` is


`y'(x)=3\sin\frac x2\cos\frac x2=\frac32\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\frac\pi2=3`

the tangent line has equation
`y=3`.