2. When E is on AD, it is 0.

y=S△AEF=(x/3)^2×S△ACB=(2/3×x^2)

Y increases with the increase of X. When x=9/5, Y is the largest, which is 54/25.

When e is on DB, it is 9/5.

y=s△aef=ae×ef/2=3(5x-x^2)/8=-3/8×(x-5/2)^2+75/32

When x=5/2, y is the largest, which is 75/32. To sum up, the maximum value of y is 75/32, and x is 5/2 at this time.

3. The circumference of 3.△ ACB is 12, and half is 6. The area is 6 and half is 3.

When F is on AC, AE=x, AF = 6-X ... If the perpendicular of AB intersects with F and AB intersects with H, then because △AHF∽△ACB.

FH=4(6-x)/5, so S △ AEF = 2 (6x-x 2)/5, and the other is 3. Solve the equation to get the x solution, which means existence.

When f is on BC, BE=5-x, then BF= 1+x, FH = 3 (x+ 1)/5. S △ BEF = 3 (4x+5-x 2)/ 10, that is, 3, equation.

Expressive power