Find the equation of a tangent line to (Differentiation)

Question

If 𝑔(𝑥) = 𝑥 + 2 cos 𝑥, then the equation of the tangent line to the graph of 𝑔(x) at 𝑥 = 𝜋 ⁄ 2 is?

Answer 1

Find the derivative of g(x)

g ' (x) = 1 - 2 sin(x)

g '(π/2) = 1-2 = -1 = m (the tangent slope at that point)

g(π/2) = π/2 + 0 = π/2 --> (x₁, y₁) = (π/2, π/2)

For the line, use the point slope form

y-y₁ = m(x-x₁) --> y -π/2 = -1(x - π/2) --> y = -x + π