Use a computer algebra system to analyze the function over the given interval. f(x)=sin(x)-(1/3)sin(3x)+(1/5)sin(5x), [0, pi) a) Find the first and second derivatives of the function. f'(x)=cos(5x)-cos(3x)+cos(x) f"(x)=? b)Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) relative maximum (x,y)=? relative minimum (x,y)=? points of inflection (there are 4): (x,y)=? (smallest x-value) (x,y)=? (smaller x-value) (x,y)=? (larger x-value) (x,y)=? (largest x-value)
Use a computer algebra system to analyze the function over the given interval. f(x)=sin(x)-(1/3)sin(3x)+(1/5)sin(5x), [0, pi) a) Find the first and second derivatives of the function. f'(x)=cos(5x)-cos(3x)+cos(x) f"(x)=? b)Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) relative maximum (x,y)=? relative minimum (x,y)=? points of inflection (there are 4): (x,y)=? (smallest x-value) (x,y)=? (smaller x-value) (x,y)=? (larger x-value) (x,y)=? (largest x-value)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use a computer algebra system to analyze the function over the given interval.
f(x)=sin(x)-(1/3)sin(3x)+(1/5)sin(5x), [0, pi)
a) Find the first and second derivatives of the function.
f'(x)=cos(5x)-cos(3x)+cos(x)
f"(x)=?
b)Find any relative extrema and points of inflection. (Round your answers to four decimal places. If an answer does not exist, enter DNE.)
relative minimum (x,y)=?
points of inflection (there are 4):
(x,y)=? (smallest x-value)
(x,y)=? (smaller x-value)
(x,y)=? (larger x-value)
(x,y)=? (largest x-value)
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