Using a tangent line approximation, determine an estimate for the cube root of 998. Include the following details in your explanation:
1. Derivation of Tangent Line: Present the process of obtaining the equation of the tangent line to the curve at a specific point.
2. Selection of Point: Specify the point on the curve chosen for the tangent line approximation, and explain the rationale behind this choice.
3. Equation of Tangent Line: Provide the equation of the tangent line and express how it approximates the curve near the chosen point.
4. Calculation: Substitute the value of 998 into the tangent line equation to calculate the approximate cube root.
5. Comparison: Discuss the accuracy of this tangent line approximation in estimating the cube root of 998 compared to the actual value.
Ensure clarity in your explanation of the tangent line approximation process.