Hi!

Solution:

Firstly, the area of the square=256, Thus, the side of the square=16.
Next we are said that the origin (0,0) is the centre i.e. all the sides are equidistant. Hence, the vertices of the square are (8,8), (-8,-8), (8,-8) & (-8,8)

Now, the second half of the question says f(x)=c$x^3$
Whenever you see a f(x) in a coordinate geometry question simply substitute f(x) with y
So, we get, y=c$x^3$
The question then says this function passes through opposite vertices of the square i.e. it passes diagonally from point (8,8)to (-8,-8) or from point (8,-8) to (-8,8)

Lets substitute the value of x &y to get c
Considering (8,8)
8=c*$8^3$
c=$\frac{1}{64}$
Similarly, when you consider (-8,-8) you get C as $\frac{1}{64}$
And when we substitute the other two values we get $\frac{-1}{64 }$. As c is a positive value we can negate the other two values

Thus, C=$\frac{1}{64}$

Hope this helps