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Lecture

# 7.1- First Derivative.pdf

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School
Department
Mathematics
Course
MATH 157
Professor
Chiaka Drake
Semester
Fall

Description
1 Chapter 7.1 Applications of the First Derivative Introduction: In the next few lectures you will be introduced to skills and concepts that will allow you to __________ the graph of any function y f (x)by __________ without using _____________________ and answer questions of _________________ such as “What is the maximum profit for a certain business enterprise?”. Monotonicity: A function y f (x) is monotonic on an interval (a,b) if it is either __________ or __________ there. Suppose x 1 and x2 are in the interval and x1 x2. f is increasing if f (x ) f (x ); 1 2 f is decreasing if f (x1) f (x2). 2 Monotonicity Test: Suppose f is a _________________ function on an _________ interval (a,b) . If f (x) 0 for all x in(a,b) , then f is ____________________ on (a,b) . If f (x) 0 for all x in(a,b) , then f is ____________________ on (a,b) . If f (x) 0 for all x in(a,b) , then f is ____________________ on (a,b) . 3 Critical Numbers (x-values): for a function f are those ______________ c in the ______________ of f such that f (c) or f (c) (__________________). The points (c, f (c))are called ______________ points. Question: How can these intervals of increase and decrease be found? Answer: 1. Find all ______________ numbers of f and all numbers where f is ________________. Place these numbers on the real number line. This ______________ the number line into open intervals. 2. ______________ a number in __________ interval. 3. ______________ the _________________ Test to these numbers to decide if f is ______________ or ______________ on these intervals. Examples Q1: Given the demand function p 300x 2x 2, find when marginal revenue is increasing. 4 Q2: For h(x) x2/3. i) Find the domain. ii) Find all intervals of increase and dec
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