MTH 151 Midterm: MTH 151 - Term Test 2

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Miami University
MTH 151
Term Test 2
Exam Guide
Calculus I
Winter 2018
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Table of Contents
Chapter 3: Differentiation Rules ..................................................................................................... 3
3.1 Polynomial and Exponential Functions ................................................................................. 3
3.2 The Product and Quotient Rules ........................................................................................... 4
3.3 Derivative of Trigonometric Functions.................................................................................. 5
3.4 Chain Rule .............................................................................................................................. 7
3.5 Implicit Differentiation ........................................................................................................ 10
3.6 Derivatives of Logarithmic Functions .................................................................................. 13
3.7 Rates of Change in the Natural and Social Sciences ........................................................... 17
3.8 Exponential Growth and Decay ........................................................................................... 20
3.9 Related Rates ....................................................................................................................... 23
Chapter 4: Applications of Differentiation .................................................................................... 27
4.1 Maximum and Minimum Values ......................................................................................... 27
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Chapter 3: Differentiation Rules
3.1 Polynomial and Exponential Functions
1.

2.

Example:
f(x) = , f’(x) = -2
3.


Example:
f(x) = 3, f’(x) = 3
4.



Example:
f(x) = 



5.
;


Past Exam Question:
1. Find f’(0) if .
Solution: 



2. A point P on the curve  is such that the tangent line at P is parallel to the line
. Find the y-coordinate of the point P.
Solution: 

Since the tangent line is parallel to , then:

When x = 1, y = 1 + 2 4 = -1.
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