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Popular Functions >

f(x)=sin^4(x)cos^2(x)

Solution

f (x) = sin^{4} (x) cos^{2} (x)

Solution

Period : π

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq \frac{4}{27}

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

Asymptotes : None

Extreme Points : Minimum (πn, 0), Maximum (arctan (2) + πn, \frac{4}{27}), Minimum (\frac{π}{2} + πn, 0), Maximum (- arctan (2) + π + πn, \frac{4}{27})

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Interval Notation

Domain : (- \infty, \infty)

Range : [0, \frac{4}{27}]

Solution steps

Periodicity of

sin^{4} (x) cos^{2} (x) : π

Domain of

sin^{4} (x) cos^{2} (x) : - \infty < x < \infty

Range of

sin^{4} (x) cos^{2} (x) : 0 \leq f (x) \leq \frac{4}{27}

Axis interception points of

sin^{4} (x) cos^{2} (x) :

X Intercepts

: (πn, 0), (\frac{π}{2} + πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin^{4} (x) cos^{2} (x) :

None

Extreme Points of

sin^{4} (x) cos^{2} (x) :

Minimum

(πn, 0),

Maximum

(arctan (2) + πn, \frac{4}{27}),

Minimum

(\frac{π}{2} + πn, 0),

Maximum

(- arctan (2) + π + πn, \frac{4}{27})

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the f(x)=sin^4(x)cos^2(x) ?
The f(x)=sin^4(x)cos^2(x) is