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Popular >

f(x)=sin^5(2x)cos^3(2x)

Solution

f (x) = sin^{5} (2 x) cos^{3} (2 x)

Solution

Period : \frac{π}{2}

Domain : - \infty < x < \infty

Range : - \frac{75 15}{4096} \leq f (x) \leq \frac{75 15}{4096}

X Intercepts : (\frac{πn}{2}, 0), (\frac{π}{4} + \frac{πn}{2}, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Minimum (\frac{π}{2} n, 0), Maximum \frac{arctan ( \frac{5}{3} )}{2} + \frac{π}{2} n, \frac{75 15}{4096}, Saddle (\frac{π}{4} + \frac{π}{2} n, 0), Minimum \frac{- arctan ( \frac{5}{3} ) + π}{2} + \frac{π}{2} n, - \frac{75 15}{4096}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{75 15}{4096}, \frac{75 15}{4096}]

Solution steps

Periodicity of

sin^{5} (2 x) cos^{3} (2 x) : \frac{π}{2}

Domain of

sin^{5} (2 x) cos^{3} (2 x) : - \infty < x < \infty

Range of

sin^{5} (2 x) cos^{3} (2 x) : - \frac{75 15}{4096} \leq f (x) \leq \frac{75 15}{4096}

Axis interception points of

sin^{5} (2 x) cos^{3} (2 x) :

X Intercepts

: (\frac{πn}{2}, 0), (\frac{π}{4} + \frac{πn}{2}, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin^{5} (2 x) cos^{3} (2 x) :

None

Extreme Points of

sin^{5} (2 x) cos^{3} (2 x) :

Minimum

(\frac{π}{2} n, 0),

Maximum

\frac{arctan ( \frac{5}{3} )}{2} + \frac{π}{2} n, \frac{75 15}{4096},

Saddle

(\frac{π}{4} + \frac{π}{2} n, 0),

Minimum

\frac{- arctan ( \frac{5}{3} ) + π}{2} + \frac{π}{2} n, - \frac{75 15}{4096}

Graph

Popular Examples

(x^{2} - 1) y^{^{'}} = 2 y

tangent of y=(x^2+1)/(3x+1),\at x=0 tangent of

y = \frac{x ^{2} + 1}{3 x + 1}, at x = 0

(\partial)/(\partial y)(Ax+By^2+Cx^2y)

\frac{\partial}{\partial y} (A x + B y^{2} + C x^{2} y)

y d x + (y - x) d y = 0

slope of (0.3)(2.5)slope

(0.3) (2.5)

Frequently Asked Questions (FAQ)

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