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Popular >

f(x)=(4x^3)/(4+3x^2-28x-60)

Solution

f (x) = \frac{4 x ^{3}}{4 + 3 x ^{2} - 28 x - 60}

Solution

Domain : x < \frac{2 ( 7 - 91 )}{3} or \frac{2 ( 7 - 91 )}{3} < x < \frac{2 ( 7 + 91 )}{3} or x > \frac{2 ( 7 + 91 )}{3}

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

X Intercepts : (0, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = \frac{2 ( 7 - 91 )}{3}, x = \frac{2 ( 7 + 91 )}{3}, Slant y = \frac{4}{3} x + \frac{112}{9}

Extreme Points : Maximum (\frac{2 ( 14 - 322 )}{3}, \frac{8 ( 385 - 23 322 )}{117}), Saddle (0, 0), Minimum (\frac{2 ( 14 + 322 )}{3}, \frac{8 ( 385 + 23 322 )}{117})

+1

Interval Notation

Domain : (- \infty, \frac{2 ( 7 - 91 )}{3}) \cup (\frac{2 ( 7 - 91 )}{3}, \frac{2 ( 7 + 91 )}{3}) \cup (\frac{2 ( 7 + 91 )}{3}, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

\frac{4 x ^{3}}{4 + 3 x ^{2} - 28 x - 60} : x < \frac{2 ( 7 - 91 )}{3} or \frac{2 ( 7 - 91 )}{3} < x < \frac{2 ( 7 + 91 )}{3} or x > \frac{2 ( 7 + 91 )}{3}

Range of

\frac{4 x ^{3}}{4 + 3 x ^{2} - 28 x - 60} : - \infty < f (x) < \infty

Axis interception points of

\frac{4 x ^{3}}{4 + 3 x ^{2} - 28 x - 60} :

X Intercepts

: (0, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{4 x ^{3}}{4 + 3 x ^{2} - 28 x - 60} :

Vertical

: x = \frac{2 ( 7 - 91 )}{3}, x = \frac{2 ( 7 + 91 )}{3},

Slant

: y = \frac{4}{3} x + \frac{112}{9}

Extreme Points of

\frac{4 x ^{3}}{4 + 3 x ^{2} - 28 x - 60} :

Maximum

(\frac{2 ( 14 - 322 )}{3}, \frac{8 ( 385 - 23 322 )}{117}),

Saddle

(0, 0),

Minimum

(\frac{2 ( 14 + 322 )}{3}, \frac{8 ( 385 + 23 322 )}{117})

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Frequently Asked Questions (FAQ)

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