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Popular Calculus >

y=3cos(x)sin(x)

Solution

y = 3 cos (x) sin (x)

Solution

Period : π

Domain : - \infty < x < \infty

Range : - \frac{3}{2} \leq f (x) \leq \frac{3}{2}

X Intercepts : (\frac{π}{2} + πn, 0), (πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{4} + πn, \frac{3}{2}), Minimum (\frac{3 π}{4} + πn, - \frac{3}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{3}{2}, \frac{3}{2}]

Solution steps

Periodicity of

3 cos (x) sin (x) : π

Domain of

3 cos (x) sin (x) : - \infty < x < \infty

Range of

3 cos (x) sin (x) : - \frac{3}{2} \leq f (x) \leq \frac{3}{2}

Axis interception points of

3 cos (x) sin (x) :

X Intercepts

: (\frac{π}{2} + πn, 0), (πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

3 cos (x) sin (x) :

None

Extreme Points of

3 cos (x) sin (x) :

Maximum

(\frac{π}{4} + πn, \frac{3}{2}),

Minimum

(\frac{3 π}{4} + πn, - \frac{3}{2})

Graph

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