If x -1, let A(x) represents the area of a region. Sketch that region. Use the r

Question

If x -1, let A(x) represents the area of a region. Sketch that region. Use the result of Exercise 28 in Section 5.2 to find an expression for A(x). Find A'(x). What do you notice? If x -1 and h is a small positive number, then A(x + h) - A(x) represents the area of a region. Describe and sketch the region. Draw a rectangle that approximates the region in part (d). By comparing the areas of these two regions, show that A(x + h) - A(x)/h 1 + x2 Use part (e) to give an intuitive explanation for the result of part (c).

Explanation / Answer

a) A'(x) = (1+x^2

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