Final answer:
To find a unit tangent vector to the level curve of a function at a specific point, calculate the derivative of the function, evaluate it at the given point, and normalize the resulting vector.
Step-by-step explanation:
The concept of a unit tangent vector relates to calculus and the study of curves. In this question, we are given a function and we are asked to find a unit tangent vector to the level curve at a specific point. The unit tangent vector represents the direction of the curve at that point.
To find a unit tangent vector, we need to calculate the derivative of the function, evaluate it at the given point, and then normalize the resulting vector. The resulting vector will have a magnitude of 1 and will point in the direction of the curve.
For example, if the function is y = f(x), we can find the derivative dy/dx. Then, the unit tangent vector at a specific point (x0, y0) is given by T = (1, dy/dx).