Sure! I would be happy to help with your review question. To find the largest area of a rectangle with a base on the x-axis and upper corners touching the parabola y=12-x^2, we can use the formula for the area of a rectangle, which is A = length x width.
In this case, the length of the rectangle will be the x-coordinate of the upper corners, and the width will be the distance between the two upper corners. Since the upper corners touch the parabola, we can set the x-coordinate of the upper corners equal to the x-coordinate of the vertex of the parabola, which is x=0.
To find the distance between the two upper corners, we can use the distance formula, which is d = √((x2-x1)^2 + (y2-y1)^2). In this case, we can set one of the upper corners to be (0,12) and the other upper corner to be (x,12-x^2). Plugging these values into the distance formula, we get d = √((x-0)^2 + ((12-x^2)-12)^2) = √(x^2 + x^4).
Now, we can plug in these values into the area formula A = length x width. A = (0)(√(x^2 + x^4)) = 0.
Since the area cannot be negative, we know that the largest area of the rectangle is when x=0, which means the rectangle is actually a square with sides of length 0. Therefore, the largest area of the rectangle is 0 units squared.
I hope this helps with your review and good luck on your test tomorrow! Let me know if you have any other questions.
