Question

15. Suppose that f(x) = x 3 − 3xy2 represents velocity potential function of certain fluid flow. Find the linear approximation of the function at the point (1, 2).​

Answer 1

Given: f(x) = x³ − 3xy² represents velocity potential function of certain fluid flow.

To find: The linear approximation of the function at the point (1, 2).​

Solution:

In the given question, the values of x and y are given as 1 and 2, respectively. In order to find the linear approximation of the function at the given point, the values of x and y must be substituted in the function equation. This can be represented in the following calculations.

$f(x) = x^{3} - 3xy^{2}$

       $= (1)^{3} - (1)(2)^{2}$

       $= 1 - 4$

       $= - 3$

So, the function is equal to -3 when x and y are replaced by 1 and 2, respectively.

Therefore, the linear approximation of the function at the point (1, 2). is -3.