Suppose f(3) = 1 and f′(3) = 4. Let g(x) = x² + f(x) and h(x) = 3f(x).
Find an equation of the line tangent to y = g(x) at x = 3.

Verified step by step guidance

1. Step 1: Identify the function g(x) and its components. We have g(x) = x^2 + f(x).
2. Step 2: To find the equation of the tangent line, we need the slope at x = 3. This requires finding g'(x), the derivative of g(x).
3. Step 3: Differentiate g(x) = x^2 + f(x) to get g'(x) = 2x + f'(x).
4. Step 4: Substitute x = 3 into g'(x) to find the slope of the tangent line: g'(3) = 2(3) + f'(3).
5. Step 5: Use the point-slope form of a line, y - y_1 = m(x - x_1), where m is the slope from Step 4, and (x_1, y_1) is the point (3, g(3)). Calculate g(3) using g(3) = 3^2 + f(3).