SOLUTION: If f(x)=sinx+cos2x,determine which sub-intervals of (0,2pi)
f(x) is increasing on and which intervals f(x) is decreasing.
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-> SOLUTION: If f(x)=sinx+cos2x,determine which sub-intervals of (0,2pi)
f(x) is increasing on and which intervals f(x) is decreasing.
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If f(x)=sinx+cos2x,determine which sub-intervals of (0,2pi)
f(x) is increasing on and which intervals f(x) is decreasing.
f(x) = sin(x) + cos(2x)
f'(x) = cos(x) - 2sin(2x)
We set f'(x)=0 to see if there are any critical
values as far as increasing or decreasing:
cos(x) - 2sin(2x) = 0
cos(x) -2[2sin(x)cos(x)] = 0
cos(x) -4sin(x)cos(x) = 0
cos(x)[1 - 4sin(x)] = 0
cos(x) = 0; 1 - 4sin(x) = 0
x = ; -4sin(x) = -1
sin(x) = 1/4
x = .2527, 2.8889
Substituting test values on each interval, we find:
It's increasing on
It's decreasing on
It's increasing on
It's decreasing on
It's increasing on
The 1st green circle on the graph is where x = 0.2527
The 2nd green circle on the graph is where x =
The 3rd green circle on the graph is where x = 2.8889
The 4th green circle on the graph is where x =
Edwin