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Popular >

f(x)=(sin(6x))^3

Solution

f (x) = (sin (6 x))^{3}

Solution

Period : \frac{π}{3}

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 1

X Intercepts : (\frac{πn}{3}, 0), (\frac{π}{6} + \frac{πn}{3}, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (\frac{π}{3} n, 0), Maximum (\frac{π}{12} + \frac{π}{3} n, 1), Saddle (\frac{π}{6} + \frac{π}{3} n, 0), Minimum (\frac{π}{4} + \frac{π}{3} n, - 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

sin^{3} (6 x) : \frac{π}{3}

Domain of

sin^{3} (6 x) : - \infty < x < \infty

Range of

sin^{3} (6 x) : - 1 \leq f (x) \leq 1

Axis interception points of

sin^{3} (6 x) :

X Intercepts

: (\frac{πn}{3}, 0), (\frac{π}{6} + \frac{πn}{3}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin^{3} (6 x) :

None

Extreme Points of

sin^{3} (6 x) :

Minimum

(\frac{π}{3} n, 0),

Maximum

(\frac{π}{12} + \frac{π}{3} n, 1),

Saddle

(\frac{π}{6} + \frac{π}{3} n, 0),

Minimum

(\frac{π}{4} + \frac{π}{3} n, - 1)

Popular Examples

y=((x+1))/((x-1))

y = \frac{( x + 1 )}{( x - 1 )}

f(x)=(x^3-8)^{2/3}

f (x) = (x^{3} - 8)^{\frac{2}{3}}

y = x^{2} + 18 x - 10

f(x)=sqrt(19-x)

f (x) = 19 - x

y = - 1 x + 5

Frequently Asked Questions (FAQ)

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