Find the lengths of the curves in Exercises 4-8. If you have graphing software, you may want to graph these curves to see what they look like. 4. x = (y^(3/2)/3) - y^(1/2) from y = 1 to y = 9 5. x = (y^4/4) + 1/(8y2) from y = 1 to y = 2 6. x = (y^3/6) + 1/(2y) from y = 2 to y = 3 7. y = (3/4)x^(4/3 )- (3/8)x^(2/3) + 5, 1<=x<= 8 8. y = (x3/3) + x2 + x + 1/(4x + 4), 0<=x<=2

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.