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3-6 ConstructFunctions

# 3-6 ConstructFunctions - Section 3.6(Sullivan 8th ed...

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Section 3.6 (Sullivan, 8 th ed.) MAC1140, MAC1147 3-6: Mathematical Models: Constructing Functions For any quadratic equation f(x) = ax 2 + bx + c, it will have its minimum or maximum at its vertex. It will be a maximum if a < 0 because the parabola will open downward; it will be a minimum if a > 0. The vertex can be found without graphing: Vertex = - - F H G I K J F H G I K J b a f b a 2 2 , . Axis of symmetry: the line x = - b a 2 . 1. Volume of a Cylinder: If the volume of a cylinder is V = π r 2 h and the height is half the radius, express the volume V as a function of r . 2. Finding the area of a rectangular field with fixed perimeter: George has 2000 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing. a) Express the area A of the rectangle as a function of x, where x is the length: b) What is the largest area? 3. A rectangle has one corner on the graph of y = 36 - x 2 , x > 0, at (x, y); another at the origin; and a third on the positive x-axis at (x, 0), and a fourth on the positive y-axis.

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3-6 ConstructFunctions - Section 3.6(Sullivan 8th ed...

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