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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 2 \leq f (x) \leq 2

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (arccos (\frac{5}{6}) + 2 πn, \frac{2 2}{3 3}), Minimum (\frac{π}{2} + 2 πn, - 2), Maximum (arccos (- \frac{5}{6}) + 2 πn, \frac{2 2}{3 3}), Minimum (- arccos (- \frac{5}{6}) + 2 π + 2 πn, - 2 \frac{1}{6} cos (2 (- arccos (- \frac{5}{6}) + 2 π))), Maximum (\frac{3 π}{2} + 2 πn, 2), Minimum (2 π - arccos (\frac{5}{6}) + 2 πn, - 2 \frac{1}{6} cos (2 (2 π - arccos (\frac{5}{6}))))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 2, 2]

Solution steps

Periodicity of

2 sin (x) cos (2 x) : 2 π

Domain of

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

Range of

2 sin (x) cos (2 x) : - 2 \leq f (x) \leq 2

Axis interception points of

2 sin (x) cos (2 x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

2 sin (x) cos (2 x) :

None

Extreme Points of

2 sin (x) cos (2 x) :

Maximum

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

Minimum

(\frac{π}{2} + 2 πn, - 2),

Maximum

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

Minimum

(- arccos (- \frac{5}{6}) + 2 π + 2 πn, - 2 \frac{1}{6} cos (2 (- arccos (- \frac{5}{6}) + 2 π))),

Maximum

(\frac{3 π}{2} + 2 πn, 2),

Minimum

(2 π - arccos (\frac{5}{6}) + 2 πn, - 2 \frac{1}{6} cos (2 (2 π - arccos (\frac{5}{6}))))

Popular Examples

y=2xtanh((2x-2)/(3x+2))

y = 2 x tanh (\frac{2 x - 2}{3 x + 2})

h(t)=-16t^2+104t+56

h (t) = - 16 t^{2} + 104 t + 56

f (x) = 5 x^{2} + 3 x + 4

y=-2x^3+3x^2+12x+15

y = - 2 x^{3} + 3 x^{2} + 12 x + 15

h (x) = e^{- x}

Frequently Asked Questions (FAQ)

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