Final answer:
To approximate a function at a point near (a,b), one could use a linear approximation with the line of best fit equation û = a + bx, where a and b minimize the sum of squared errors.
Step-by-step explanation:
To approximate a function f at a point near (a,b), one can use the equation of a line or a linear approximation. This involves knowing the values of the function, its first derivative (slope), and a given point through which the line passes. From the provided information, we have the following reference equation for the line of best fit: û = a + bx. Here, a and b are constants that can be chosen to minimize the sum of squared errors (SSE), which measures the overall distance of data points from the line of best fit.
Once the values of a and b are determined, we can then calculate the approximation of f near (a,b) using those constants, especially when f represents a simple relationship between variables, such as a horizontal line where f(x) = 20 within the domain 0 ≤ x ≤ 20.