1. **State the problem:** Find the equation of the tangent line to the function $f(x) = 3 \sec(x)$ at $x = 0$. 2. **Recall the formula for the tangent line:** The tangent line to $y = f(x)$ at $x = a$ is given by $$y = f(a) + f'(a)(x - a)$$ where $f'(a)$ is the derivative of $f(x)$ evaluated at $x = a$. 3. **Find $f(0)$:** $$f(0) = 3 \sec(0) = 3 \times 1 = 3$$ 4. **Find the derivative $f'(x)$:** Recall that $\frac{d}{dx} \sec(x) = \sec(x) \tan(x)$, so $$f'(x) = 3 \frac{d}{dx} \sec(x) = 3 \sec(x) \tan(x)$$ 5. **Evaluate $f'(0)$:** $$f'(0) = 3 \sec(0) \tan(0) = 3 \times 1 \times 0 = 0$$ 6. **Write the tangent line equation:** Using $a=0$, $$y = f(0) + f'(0)(x - 0) = 3 + 0 \times x = 3$$ **Final answer:** The equation of the tangent line at $x=0$ is $$y = 3$$