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Popular >

f(x)=sin^4(x)+cos^4(x)-1

Solution

f (x) = sin^{4} (x) + cos^{4} (x) - 1

Solution

Period : π

Domain : - \infty < x < \infty

Range : - \frac{1}{2} \leq f (x) \leq 0

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

Asymptotes : None

Extreme Points : Maximum (πn, 0), Minimum (\frac{π}{4} + πn, - \frac{1}{2}), Maximum (\frac{π}{2} + πn, 0), Minimum (\frac{3 π}{4} + πn, - \frac{1}{2})

+1

Solution steps

Periodicity of

sin^{4} (x) + cos^{4} (x) - 1 : π

Domain of

sin^{4} (x) + cos^{4} (x) - 1 : - \infty < x < \infty

Range of

sin^{4} (x) + cos^{4} (x) - 1 : - \frac{1}{2} \leq f (x) \leq 0

Axis interception points of

sin^{4} (x) + cos^{4} (x) - 1 :

X Intercepts

: (πn, 0), (\frac{π}{2} + πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin^{4} (x) + cos^{4} (x) - 1 :

None

Extreme Points of

sin^{4} (x) + cos^{4} (x) - 1 :

Maximum

(πn, 0),

Minimum

(\frac{π}{4} + πn, - \frac{1}{2}),

Maximum

(\frac{π}{2} + πn, 0),

Minimum

(\frac{3 π}{4} + πn, - \frac{1}{2})

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Frequently Asked Questions (FAQ)

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