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Popular >

inflection (x^2)/(x^2+27)

Solution

inflection points

\frac{x ^{2}}{x ^{2} + 27}

Solution

(- 3, \frac{1}{4}), (3, \frac{1}{4})

Solution steps

f^{''} (x) = \frac{162 ( - x ^{2} + 9 )}{( x ^{2} + 27 ) ^{3}}

Find intervals:

Concave Downward

: - \infty < x < - 3,

Concave Upward

: - 3 < x < 3,

Concave Downward

: 3 < x < \infty

Plug

x = - 3

into

\frac{x ^{2}}{x ^{2} + 27} : \frac{1}{4}

(- 3, \frac{1}{4})

Plug

x = 3

into

\frac{x ^{2}}{x ^{2} + 27} : \frac{1}{4}

(3, \frac{1}{4})

(- 3, \frac{1}{4}), (3, \frac{1}{4})

Popular Examples

slope of (6.4) 3/2 slope

(6.4) \frac{3}{2}

intercepts of f(x)=(x-7)/2 intercepts

f (x) = \frac{x - 7}{2}

range of (x^2-2)/(x+2)range

\frac{x ^{2} - 2}{x + 2}

parallel 3y=5x+7 parallel

3 y = 5 x + 7

domain of y=3tan(4x+6)-3 domain

y = 3 tan (4 x + 6) - 3

Frequently Asked Questions (FAQ)

What is the inflection (x^2)/(x^2+27) ?
The inflection (x^2)/(x^2+27) is (-3, 1/4),(3, 1/4)