Find the antiderivative function, the graph of which passes through the point f (x) = 4-x ^ 2: (- 3; 10)

Initially, we find the general view of the antiderivatives for the function, then substitute the coordinate values into the general view of the antiderivatives.

y = 4 – x ^ 2.

To find the general form of antiderivatives, add a variable to the first term, and increase the variable in the variable of the second term.

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

Now we substitute the coordinates of the point (-3; 10), which belongs to the graph of the function:

10 = 4 * (-3) – 4/3 * (-27) + C;

10 = -12 + 36 + C;

C = 10 – 24 = -14.

y = 4 * x – 4/3 * x ^ 3 – 14 – function formula.