Final answer:
The equation of the tangent line to the function g(x) = 2x sin(x) at x = π is y = 0, as the slope of the tangent line at that point is 0.
Step-by-step explanation:
To find the equation of the tangent line to the given function g(x) = 2x sin(x) at x = π, we need to calculate the derivative of g(x) to get the slope of the tangent line at that point. The derivative g'(x) can be found using the product rule for differentiation, which in this case is:
g'(x) = d/dx(2x sin(x)) = 2 sin(x) + 2x cos(x)
Next, we evaluate the derivative at x = π:
g'(π) = 2 sin(π) + 2π cos(π) = 0 + 0 = 0
The slope of the tangent line at x = π is 0, so the tangent line is horizontal. Since g(π) = 2π sin(π) = 0, the point of tangency is (π, 0). Therefore, the equation of the tangent line is simply y = 0.