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Unformatted text preview: WORKSHEET 23 - Fall 1995 1. Let h be a differentiable function whose tangent line at the point (2 , h (2)) is y = 3 x 12. Let g be the function defined by g ( x ) = h (8 x 2 ). a) What is g ( 1 2 )? b) Find the equation of the tangent line to g at the point ( 1 2 , g ( 1 2 )). 2. Let f be differentiable at a . Let c and k be constants. Assume that the polynomial q ( x ) = c + kx has the property that q ( a ) = f ( a ) and q ( a ) = f ( a ). Prove that q ( x ) = f ( a ) + f ( a )( x a ) . What is the significance of this result? 3. At Pizza Hut, they deliver pizzas in fancy boxes formed from rectangular pieces of cardboard which are 95 cm by 47 cm. To form a box, eight squares of equal size are cut out, four along each 95 cm side. In the picture below the squares are removed from the left, middle, and two side by side from the right (to form a lip for the box.) The box is then folded in the obvious manner. (Imagine a pizza box.) What is the largest volume which can be obtained this way? How do you do it? Does Pizza Hutbox....
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
- Spring '08