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Popular >

y=tan^3(x)-tan(x)

Solution

y = tan^{3} (x) - tan (x)

Solution

Period : π

Domain : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range : - \infty < f (x) < \infty

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

Asymptotes : Vertical x = \frac{π}{2} + πn

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

+1

Interval Notation

Domain : [πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Range : (- \infty, \infty)

Solution steps

Periodicity of

tan^{3} (x) - tan (x) : π

Domain of

tan^{3} (x) - tan (x) : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range of

tan^{3} (x) - tan (x) : - \infty < f (x) < \infty

Axis interception points of

tan^{3} (x) - tan (x) :

X Intercepts

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

Y Intercepts

: (0, 0)

Asymptotes of

tan^{3} (x) - tan (x) :

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

tan^{3} (x) - tan (x) :

Minimum

(\frac{π}{6} + πn, - \frac{2}{3 3}),

Maximum

(\frac{5 π}{6} + πn, \frac{2}{3 3})

Popular Examples

f(x)=x^2-38x-324

f (x) = x^{2} - 38 x - 324

y=6x-2x^2+x^2-x

y = 6 x - 2 x^{2} + x^{2} - x

g (x) = 3 + 3 cos (x)

y = (x + 2)^{2} x

f (m) = m^{2} + 6 m + 6

Frequently Asked Questions (FAQ)

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