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Popular >

f(x)=2cos(x)+sin(2x)

Solution

f (x) = 2 cos (x) + sin (2 x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

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

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), Y Intercepts : (0, 2)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{6} + 2 πn, 3 + \frac{3}{2}), Minimum (\frac{5 π}{6} + 2 πn, - 3 - \frac{3}{2}), Saddle (\frac{3 π}{2} + 2 πn, 0)

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Interval Notation

Domain : (- \infty, \infty)

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

Solution steps

Periodicity of

2 cos (x) + sin (2 x) : 2 π

Domain of

2 cos (x) + sin (2 x) : - \infty < x < \infty

Range of

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

Axis interception points of

2 cos (x) + sin (2 x) :

X Intercepts

: (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0),

Y Intercepts

: (0, 2)

Asymptotes of

2 cos (x) + sin (2 x) :

None

Extreme Points of

2 cos (x) + sin (2 x) :

Maximum

(\frac{π}{6} + 2 πn, 3 + \frac{3}{2}),

Minimum

(\frac{5 π}{6} + 2 πn, - 3 - \frac{3}{2}),

Saddle

(\frac{3 π}{2} + 2 πn, 0)

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Frequently Asked Questions (FAQ)

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