Question

How do you find the slope of the tangent line to the graph of the given function `y=sinx+3`; `x=pi`?

Answer 1

You can take the derivative, and plug in `x = pi`.

`[(df(pi))/(dx)] = [cosx + 0]|_(x=pi) = cospi = -1`

The slope of a tangent line at `x = a` is always just the derivative of the function evaluated at `x = a`, while `d/(dx)[sinu] = cosu((du)/(dx))` (Chain Rule).