SOLUTION: A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point (x,y) on the parabola. Write a formula for the function A(x) that gives the area of the recta

Question 43815This question is from textbook Algebra and trigonometry with analytic geometry
: A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point (x,y) on the parabola. Write a formula for the function A(x) that gives the area of the rectangle as a function of the x-coordinate of the point chosen. Ok so far this one has given me some trouble trying to work out. Came up with answer of f(x)= 6(27-3x^2) it this right. This question is from textbook Algebra and trigonometry with analytic geometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point (x,y) on the parabola. Write a formula for the function A(x) that gives the area of the rectangle as a function of the x-coordinate of the point chosen. Ok so far this one has given me some trouble trying to work out. Came up with answer of f(x)= 6(27-3x^2) it this right.
I assume you put this on a coordinate system; then chose a point (x,y)
on the parabola; then drew the rectangle symmetric to the y-axis.
The area of the rectangle = (2x)y
=2x(27-3x^2)
=54x-6x^3
Cheers,
Stan H.
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