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Popular Calculus >

f(x)=(4x^2-1)/(x^3)

Solution

f (x) = \frac{4 x ^{2} - 1}{x ^{3}}

Solution

Domain : x < 0 or x > 0

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

X Intercepts : (\frac{1}{2}, 0), (- \frac{1}{2}, 0)

Asymptotes : Vertical x = 0, Horizontal y = 0

Extreme Points : Minimum (- \frac{3}{2}, - \frac{16}{3 3}), Maximum (\frac{3}{2}, \frac{16}{3 3})

+1

Interval Notation

Domain : (- \infty, 0) \cup (0, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

\frac{4 x ^{2} - 1}{x ^{3}} : x < 0 or x > 0

Range of

\frac{4 x ^{2} - 1}{x ^{3}} : - \infty < f (x) < \infty

Axis interception points of

\frac{4 x ^{2} - 1}{x ^{3}} :

X Intercepts

: (\frac{1}{2}, 0), (- \frac{1}{2}, 0)

Asymptotes of

\frac{4 x ^{2} - 1}{x ^{3}} :

Vertical

: x = 0,

Horizontal

: y = 0

Extreme Points of

\frac{4 x ^{2} - 1}{x ^{3}} :

Minimum

(- \frac{3}{2}, - \frac{16}{3 3}),

Maximum

(\frac{3}{2}, \frac{16}{3 3})

Graph

Popular Examples

area x=sqrt(1/(12y)),y=x,x=16y

(\partial)/(\partial x)(-(x/y))

derivative of x/(4-sqrt(16-x^2))

tangent of f(x)=5-2x^2,(-5,-45)

integral from 0 to 2 of (1+x)^{1/3}*2

Frequently Asked Questions (FAQ)

What is the f(x)=(4x^2-1)/(x^3) ?
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