F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)

d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.

4 0

3 years ago

list the next nine multiples of each number Find the common multiples. Multiples of 4: 4, Multiples of 7:7, Common multiples: Mu

Alenkinab [10]

3 : 3,6,9,12,15,18,21,24,27,30

4 : 4,8,12,16,20,24,28,32,36

7: 7,14,21,28,35,42,49,56,63

9: 9,18,27,36,45,54,63,72,81

6 0

3 years ago

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