A ray has only one endpoint and goes on forever in the other direction. A segment has two endpoints
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.
I see. Imagine you have f(x)=|x|. It's a V shaped graph.
Now if f(x)=|x|, 2f(x)=2|x|.
Graph Transformation Rule:
af(x), multiply y-coordinates by a.
*Ultimately, you'd still have a V shaped graph in 2f(x)=2|x|, but the y values of all the coordinates in f(x)=|x| would have to be multiplied by 2 giving you 2f(x)=2|x|.
Answer:
15/
x
136
Step-by-step explanation:
im pretty sure
