Find the antiderivative F (x) for the function f (x) = 2√x, the graph of which passes through the point A (0; 7/8).

To begin with, we will find the general form of the antiderivatives for the function, and then we will determine the exact antiderivative by substituting the values of the coordinates of the point in the formula.

Given a function:

y = 2 * x ^ (1/2).

To find the antiderivative, raise the degree of the variable by one:

F (x) = x ^ (3/2) * 4/3 + C, where C is const.

Substitute the values of the coordinates of the point belonging to the graph of the antiderivative:

7/8 = 4/3 * 0 ^ (3/2) + C;

7/8 = C.

Accordingly, our antiderivative has the formula:

y = 4/3 * x ^ (3/2) + 7/8.