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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{2}{3 3} \leq f (x) \leq \frac{2}{3 3}

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

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

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Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{2}{3 3}, \frac{2}{3 3}]

Solution steps

Periodicity of

- sin (x) cos^{2} (x) : 2 π

Domain of

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

Range of

- sin (x) cos^{2} (x) : - \frac{2}{3 3} \leq f (x) \leq \frac{2}{3 3}

Axis interception points of

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

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

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

None

Extreme Points of

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

Minimum

(arccos (\frac{2}{3}) + 2 πn, - \frac{2}{3 3}),

Maximum

(\frac{π}{2} + 2 πn, 0),

Minimum

(arccos (- \frac{2}{3}) + 2 πn, - \frac{2}{3 3}),

Maximum

(- arccos (- \frac{2}{3}) + 2 π + 2 πn, \frac{2}{3 3}),

Minimum

(\frac{3 π}{2} + 2 πn, 0),

Maximum

(2 π - arccos (\frac{2}{3}) + 2 πn, \frac{2}{3 3})

Popular Examples

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f (x) = \frac{1}{1 - e ^{\frac{x}{1 - x}}}

f(x)=(x^2-6x+8)e^{x/2}

f (x) = (x^{2} - 6 x + 8) e^{\frac{x}{2}}

f(x)=x^3-3x^2+2x-8

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

f(x)=(3x^2)(x^{1/2})

f (x) = (3 x^{2}) (x^{\frac{1}{2}})

f(x)=(tan^2(x))/2

f (x) = \frac{tan ^{2} ( x )}{2}

Frequently Asked Questions (FAQ)

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