Area Find the area of the largest rectangle that can be inscribed under the curve in the first and second quadrants.
To calculate: The largest area of a rectangle that can fit inside the provided curve and the x-axis.
For a function f that is twice differentiable on an open interval I, if for some c, then,
If the function f has relative minima at c if the function f has relative maxima at c.
The provided curve is a bell curve. So the rectangle would be of the form:
Let the point lie on the intersection of the curve and the rectangle. From the symmetry of the bell curve, the other intersection point in the second quadrant would be . This implies the length of the rectangle would be 2x and the breadth would be .
Hence, the area can be written as:
Differentiate the provided function with respect to x and equate that to 0 to get the critical point.
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