M1550-Exam2-Study-Guide

M1550-Exam2-Study-Guide - Math 1550 (30) Exam 2 Study Guide...

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Math 1550 (30) Exam 2 Study Guide Exam 2 will be on Thursday, October 7th, from 4:30 - 5:30. These problems should be a guide to prepare for the test. 1. Use the deﬁnition of the derivative to ﬁnd f 0 ( x ), for: a) f ( x ) = 2 x 2 + 1 b) f ( x ) = x c) f ( x ) = 3 x - 4 2. Find all values of x where the tangent lines to y = x 3 and y = x 4 are parallel. 3. Find all values of x where the tangent lines to y = x 2 and y = x are perpendicular. 4. Determine the coeﬃcients a,b such that p ( x ) = x 2 + ax + b satisﬁes p (1) = 15 and p 0 (1) = 8. 5. Suppose that: f ( x + h ) - f ( x ) = - 3 hx 2 + 2 hx + h 2 x - 6 h 2 + 3 h 3 Find f 0 ( x ). 6. Calculate F 0 (0), where: F ( x ) = 6 x 7 + x 5 + 2 x 3 + 7 x 7 x 7 - 6 x 9 + 9 x 3 - 10 [Hint: You don’t need to ﬁnd the general expression for F 0 ( x ), you only need to ﬁnd F 0 (0).] 7. Find: a) d dt ± 1 - t 2 2 + t 2 ² b) d dx ± e x x 2 + 12 ² 1

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c) d dt ( ( t 2 + 1) e t ) 8. Find the equation for the line tangent to the graph of f ( x ) = - 5 xe x at the point (
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This note was uploaded on 12/29/2011 for the course MATH 1550 taught by Professor Wei during the Fall '08 term at LSU.

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M1550-Exam2-Study-Guide - Math 1550 (30) Exam 2 Study Guide...

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