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ENGINEERING MATHEMATICS APPLICATION OF DERIVATIVES
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Chapter 4Applications of Derivatives
Extreme Values of Functions
The Rolles TheoremThe mean value theorem
Monotonic Functions and the first derivative testExample:
Find the critical points of and identify the intervals on which f is increasing and decreasing.Solution:
Example:
Find the critical points of and identify the intervals on which f is increasing and decreasing. Find the functions local and absolute extreme values.Solution:
First derivative test for local extrema:
x=0 : f(x) does not change sign
x=1 :f(x) changes from ve to +ve
Local min: f(1)=-3Absolute min: f(1)=-3No local extremumlocal minimum
Tutorial 4Exercises 3.7: 11,25,34,45Exercises 3.8: 20,28,32,41Exercises 4.1: 23,43,48,51,64Exercises 4.2: 4,11Exercises 4.3: 4,18,28,38,47Ref: Thomas Calculus, 12th Edition