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domyy
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Homework Statement
1. f(x) = 5 sin (8∏x)
2. g(x) = 4∏ [ cos (3∏x) sin (3∏x)]
3. h(x) = cos [sec (5∏x)]
4. Sketch the graph of each function on the indicated interval, making use of relative extrema and points of inflection.
f(x) = 2sinx + sin2x ; [0,2∏]
The Attempt at a Solution
1. f(x) = 5 sin (8∏x)
f'(x) = 5 cos (8∏x) . (8∏)
f'(x) = 40∏ cos (8∏x)[/COLOR]
2. g(x) = 4∏ [ cos (3∏x) sin (3∏x)]
g'(x) = 4∏ {[cos (3∏x)][(sin (3∏x)]' + [sin (3∏x)][cos (3∏x)]'}
g'(x) = 4∏ {[cos (3∏x)][cos (3∏x) . 3∏ ] + [ sin (3∏x)][ -sin (3∏x) . 3∏ ]}
g'(x) = 12∏ cos2 (3∏x) -12∏ sin2 (3∏x)
3. h(x) = cos [sec(5∏x)]
h'(x) = -sin [ sec(5∏x) . 5∏][ tan (5∏x) . 5∏]
h'(x) = -25∏ sec (5∏x) tan(5∏x)[/COLOR]
4. Sketch the graph of each function on the indicated interval, making use of relative extrema and points of inflection.
f(x) = 2sinx + sin2x
f'(x) = 2cosx + cos2x . 2
f'(x) = 2cosx + 2cos(2x)
=> f'(x) = 0
2cosx + 2cos(2x) = 0
Now, how to proceed from here?
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