a.
To find: third order Taylor polynomial for f at x=3 and use it to approximate f(3.2)
a.
Answer to Problem 55RE
1.936
Explanation of Solution
Given: f(3)=1,f’(3)=4,f’’(3)=6,f’’’(3)=12,a=3
Concept Used:
Calculation:
Conclusion: the approximate of f(3.2)=1.936
b.
To find: to find second order Taylor polynomial for f’ at x=3
b.
Answer to Problem 55RE
2.74
Explanation of Solution
Given: f(3)=1,f’(3)=4,f’’(3)=6,f’’’(3)=12,a=3Concept Used:
Calculation:
Conclusion: the approximation of f’(2.7) is 2.74
iii.
To justify: if linearization of f underestimate or overestimate the value of f(x) near x=3
iii.
Answer to Problem 55RE
underestimates
Explanation of Solution
Given: f’’(x)=6
Concept Used: if second derivative is positive the it is underestimate
Calculation:
f’’(x)=6>0 therefore it is underestimate
Conclusion: f(x) is underestimate near x=3.
Chapter 9 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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