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Popular >

extreme f(x)=x^2sqrt(4-x^2)

Solution

extreme points

f (x) = x^{2} 4 - x^{2}

Solution

Minimum (- 2, 0), Maximum (- \frac{2 2}{3}, \frac{16}{3 3}), Minimum (0, 0), Maximum (\frac{2 2}{3}, \frac{16}{3 3}), Minimum (2, 0)

Solution steps

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

Find intervals:

Increasing

: - 2 < x < - \frac{2 2}{3},

Decreasing

: - \frac{2 2}{3} < x < 0,

Increasing

: 0 < x < \frac{2 2}{3},

Decreasing

: \frac{2 2}{3} < x < 2

Plug

x = - 2

into

x^{2} 4 - x^{2} : 0

Minimum (- 2, 0)

Plug

x = - \frac{2 2}{3}

into

x^{2} 4 - x^{2} : \frac{16}{3 3}

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

Plug

x = 0

into

x^{2} 4 - x^{2} : 0

Minimum (0, 0)

Plug

x = \frac{2 2}{3}

into

x^{2} 4 - x^{2} : \frac{16}{3 3}

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

Plug

x = 2

into

x^{2} 4 - x^{2} : 0

Minimum (2, 0)

Minimum (- 2, 0), Maximum (- \frac{2 2}{3}, \frac{16}{3 3}), Minimum (0, 0), Maximum (\frac{2 2}{3}, \frac{16}{3 3}), Minimum (2, 0)

Popular Examples

domain of sqrt(1/x-1)domain

\frac{1}{x} - 1

domain of f(x)=sqrt(-x)+3 domain

f (x) = - x + 3

inverse of f(x)=5-8x inverse

f (x) = 5 - 8 x

asymptotes of f(x)=(5e^x)/(e^x-4)asymptotes

f (x) = \frac{5 e ^{x}}{e ^{x} - 4}

y = x

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^2sqrt(4-x^2) ?
The extreme f(x)=x^2sqrt(4-x^2) is