Let the intersection of the parabola y = 4-x2 and the straight line y = 3x be A.B. point P moves from a to B on the arc of the parabola. (1) find the coordinates of point P when the area of the triangle PAB is the largest. (2) prove that the figure enclosed by the parabola y = 4-x2 and the straight line y = 3x is divided into two parts of equal area by the straight line x = a

Let the intersection of the parabola y = 4-x2 and the straight line y = 3x be A.B. point P moves from a to B on the arc of the parabola. (1) find the coordinates of point P when the area of the triangle PAB is the largest. (2) prove that the figure enclosed by the parabola y = 4-x2 and the straight line y = 3x is divided into two parts of equal area by the straight line x = a

When the distance from point P to AB is the largest, the area of the triangle is the largest (according to the fact that the area of the triangle is equal to half of the base multiplied by the height)
Let's do the parallel line L of ab. when l is tangent to the parabola, the tangent point is the required point P
The second question is to first express the area of the two parts in mathematical equation, and then see if this x = a exists. If it exists, we will prove that if it does not exist, it means that x = a cannot be divided into two parts with equal area