f(x)=3 sin x + 3 cos x, 0</x</2pi Find the interval of and decrease Find the loc

Q: f(x)=3 sin x + 3 cos x, 0

f'(x) = 3cos(x) - 3sin(x), now set f'(x) = 0 to find the local extrema. 3cos(x) - 3sin(x) = 0 --> cos(x) = sin(x) --> tan(x) = 1 --> p/4 or 5p/4 radians. f''(x) = -3sin(x) - 3cos(x) and set f''(x) = 0 to find points of inflection. -3sin(x) - 3cos(x) = 0 --> sin(x) = cos(x) --> x = p/4 or 5p/4 radians (again). Pick one point from each interval (0,p/4), (p/4, 5p/4), and (5p/4,2p) to see if f''(x) is positive (concave up) or negative (concave down).

ID: 3189756 • Letter: F

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f(x)=3 sin x + 3 cos x, 0</x</2pi Find the interval of and decrease Find the local min and max Find the inflection poinincrease ts Find where it concaves up and down

Explanation / Answer

f'(x) = 3cos(x) - 3sin(x), now set f'(x) = 0 to find the local extrema. 3cos(x) - 3sin(x) = 0 --> cos(x) = sin(x) --> tan(x) = 1 --> p/4 or 5p/4 radians. f''(x) = -3sin(x) - 3cos(x) and set f''(x) = 0 to find points of inflection. -3sin(x) - 3cos(x) = 0 --> sin(x) = cos(x) --> x = p/4 or 5p/4 radians (again). Pick one point from each interval (0,p/4), (p/4, 5p/4), and (5p/4,2p) to see if f''(x) is positive (concave up) or negative (concave down).

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f(x)=3 sin x + 3 cos x, 0</x</2pi Find the interval of and decrease Find the loc

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