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Popular >

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

Solution

inflection points

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

Solution

\frac{2 - 2}{ln ( 2 )}, \frac{2 ^{\frac{l n ( 2 ) + 2 - 2}{l n ( 2 )}} ( 3 - 2 2 )}{ln ^{2} ( 2 )}, \frac{2 + 2}{ln ( 2 )}, \frac{2 ^{\frac{l n ( 2 ) - 2 - 2}{l n ( 2 )}} ( 3 + 2 2 )}{ln ^{2} ( 2 )}

Solution steps

f^{''} (x) = \frac{2 - 4 ln ( 2 ) x + ln ^{2} ( 2 ) x ^{2}}{2 ^{x}}

Find intervals:

Concave Upward

: - \infty < x < \frac{- 2 + 2}{ln ( 2 )},

Concave Downward

: \frac{- 2 + 2}{ln ( 2 )} < x < \frac{2 + 2}{ln ( 2 )},

Concave Upward

: \frac{2 + 2}{ln ( 2 )} < x < \infty

Plug

x = \frac{2 - 2}{ln ( 2 )}

into

\frac{x ^{2}}{2 ^{x}} : \frac{2 ^{\frac{l n ( 2 ) + 2 - 2}{l n ( 2 )}} ( 3 - 2 2 )}{ln ^{2} ( 2 )}

\frac{2 - 2}{ln ( 2 )}, \frac{2 ^{\frac{l n ( 2 ) + 2 - 2}{l n ( 2 )}} ( 3 - 2 2 )}{ln ^{2} ( 2 )}

Plug

x = \frac{2 + 2}{ln ( 2 )}

into

\frac{x ^{2}}{2 ^{x}} : \frac{2 ^{\frac{l n ( 2 ) - 2 - 2}{l n ( 2 )}} ( 3 + 2 2 )}{ln ^{2} ( 2 )}

\frac{2 + 2}{ln ( 2 )}, \frac{2 ^{\frac{l n ( 2 ) - 2 - 2}{l n ( 2 )}} ( 3 + 2 2 )}{ln ^{2} ( 2 )}

\frac{2 - 2}{ln ( 2 )}, \frac{2 ^{\frac{l n ( 2 ) + 2 - 2}{l n ( 2 )}} ( 3 - 2 2 )}{ln ^{2} ( 2 )}, \frac{2 + 2}{ln ( 2 )}, \frac{2 ^{\frac{l n ( 2 ) - 2 - 2}{l n ( 2 )}} ( 3 + 2 2 )}{ln ^{2} ( 2 )}

Popular Examples

domain of f(x,y)=(5x)/(ln(x^2-4))domain

f (x, y) = \frac{5 x}{ln ( x ^{2} - 4 )}

range of sqrt(4x-5)range

4 x - 5

y = 4 x + 3

domain of f(x)=2(3)^x domain

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

global 0.001x global extreme points

0.001 x

Frequently Asked Questions (FAQ)

What is the inflection f(x)=(x^2)/(2^x) ?
The inflection f(x)=(x^2)/(2^x) is