Final answer:
To find a numerical approximation for the function f(x) with the given properties, we can use a linear approximation.
Step-by-step explanation:
To find a numerical approximation for the function f(x) with the properties that f(0) = 1 and f'(0) = 2, we can use a linear approximation. Since f'(0) = 2, we know that the slope of the tangent line at x = 0 is 2. This means that the function is increasing at a rate of 2 units per unit increase in x near x = 0.
Therefore, one possible approximation for the function is f(x) = 2x + 1. This equation represents a line with a slope of 2 and a y-intercept of 1, which satisfies the given conditions.
For example, when x = 0, f(x) = 1, and when x = 1, f(x) = 3. This shows that the function is increasing at a rate of 2 units per unit increase in x, as desired.