Question

Find the equation of the tangent line to the graph of `y = sin2(πx3/6)` at the point with `x = 1`?

Answer 1

Equation of tangent at `x=1)` is `y= -pi(x-1)`

Explanation:

`y=sin 2(pi x 3/6)=sin (pi x )`. At `x=1`

`y(1)= sin pi =0 :.` The point is `(1,0)`

`y=sin(pi x):.` Derivative `y'= pi cos( pi x)`

At `x=1` the slope is `m=y'= pi cos (pi) = -pi`

So equation of tangent at point `(1,0)` in point slope form is

`y-0= m(x-1) or y= -pi(x-1)`