Find the maximum value:

Question

trojanpoem · Answer

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trojanpoem · Answer

I manged to get the minimum value which is x = 2
now I am stuck with the maximum value
f(x) = 3/2 * x^2 -6x + 72

mathmath333 · Answer

is $\square ABCD$ a rectangle, parallelogram $\cdots$ ?

trojanpoem · Answer

neither rectangle nor parallelogram. It's a square of side length = 12 cm.

mathmath333 · Answer

and u want maximum value of which thing  ?

trojanpoem · Answer

We went the maximum and minimum values for the area of the triangle inscribed inside the square.

trojanpoem · Answer

I supposed that It would be the area of square - 3 triangles and got the equation above.

mathmath333 · Answer

and $AE=x$ and $FB=3x$ that's the only information given

trojanpoem · Answer

The side length of the square is 12 cm

trojanpoem · Answer

Oo , but the book answer keys says that the minimum value is at 2 when the area = 66 and the maximum at two points and the area  is 72.

trojanpoem · Answer

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area = 144 - 6x - 6(12 - 3x) - 0.5 * 3x * (12-x)
area = 3/2 x^2 - 6x + 72
da/dx = 3x -6   when da/dx = 0
x = 2
area= 66 cm^2