Application of DerivativeHard

Question

Four points A, B, C, D lie in that order on the parabola y = ax2 + bx + c. The coordinates of A, B & D are known as A(- 2, 3); B(- 1, 1) and D (2, 7). The coordinates of C for which the area of the quadrilateral ABCD is greatest, is

Options

A.(1/2, 7/4)
B.(1/2, - 7/4)
C.(-1/2, 7/4)
D.none

Solution

      
A(- 2, 3)    ⇒    3 = 4a - 2b + c
B(- 1, 1)    ⇒    1 = a - b + c
D(2, 7)     ⇒   7 = 4a + 2b + c
                ⇒   y = x2 + x + 1
C (h, h2 + h + 1),    - 1 < h < 2
Area = 3/2  (- h2 + h + 6)
Maximum at h = 1/2     ⇒    C

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