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Popular >

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

Solution

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

Solution

Period : π

Domain : - \infty < x < \infty

Range : \frac{1}{2} \leq f (x) \leq 1

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (πn, 1), Minimum (\frac{π}{4} + πn, \frac{1}{2}), Maximum (\frac{π}{2} + πn, 1), Minimum (\frac{3 π}{4} + πn, \frac{1}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{2}, 1]

Solution steps

Periodicity of

sin^{4} (x) + cos^{4} (x) : π

Domain of

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

Range of

sin^{4} (x) + cos^{4} (x) : \frac{1}{2} \leq f (x) \leq 1

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(πn, 1),

Minimum

(\frac{π}{4} + πn, \frac{1}{2}),

Maximum

(\frac{π}{2} + πn, 1),

Minimum

(\frac{3 π}{4} + πn, \frac{1}{2})

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Frequently Asked Questions (FAQ)

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