extreme f(x)=xsqrt(3x-x^2)

Solución

puntos extremos

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

M \overset{ı}{ˊ} nimo (0, 0), M \overset{a}{ˊ} ximo (\frac{9}{4}, \frac{27 3}{16}), M \overset{ı}{ˊ} nimo (3, 0)

Pasos de solución

f^{'} (x) = \frac{- 4 x ^{2} + 9 x}{2 3 x - x ^{2}}

Encontrar intervalos:

Creciente

: 0 < x < \frac{9}{4},

Decreciente

: \frac{9}{4} < x < 3

Ingrese

x = 0

x 3 x - x^{2} : 0

M \overset{ı}{ˊ} nimo (0, 0)

Ingrese

x = \frac{9}{4}

x 3 x - x^{2} : \frac{27 3}{16}

M \overset{a}{ˊ} ximo (\frac{9}{4}, \frac{27 3}{16})

Ingrese

x = 3

x 3 x - x^{2} : 0

M \overset{ı}{ˊ} nimo (3, 0)

M \overset{ı}{ˊ} nimo (0, 0), M \overset{a}{ˊ} ximo (\frac{9}{4}, \frac{27 3}{16}), M \overset{ı}{ˊ} nimo (3, 0)