What is the extreme f(x)=x^3(x-6)^4 ?

The extreme f(x)=x^3(x-6)^4 is Saddle(0,0),Maximum(18/7 , 1934917632/823543),Minimum(6,0)

Popular >

extreme f(x)=x^3(x-6)^4

extreme points

f (x) = x^{3} (x - 6)^{4}

Saddle (0, 0), Maximum (\frac{18}{7}, \frac{1934917632}{823543}), Minimum (6, 0)

Solution steps

f^{'} (x) = x^{2} (x - 6)^{3} (7 x - 18)

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{18}{7},

Decreasing

: \frac{18}{7} < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 0

into

x^{3} (x - 6)^{4} : 0

Saddle (0, 0)

Plug

x = \frac{18}{7}

into

x^{3} (x - 6)^{4} : \frac{1934917632}{823543}

Maximum (\frac{18}{7}, \frac{1934917632}{823543})

Plug

x = 6

into

x^{3} (x - 6)^{4} : 0

Minimum (6, 0)

Saddle (0, 0), Maximum (\frac{18}{7}, \frac{1934917632}{823543}), Minimum (6, 0)

f (x) = \frac{2}{3} x^{3} - 2 x^{2} + \frac{44}{3}

f (x) = 2 x^{3} - 24 x^{2} + 72 x + 7

y = x^{2} lo g_{6} (x)

f (x) = x x^{2} + 9

f (x) = (x + 1)^{2} (x - 4)^{5} (x - 7)^{4}

What is the extreme f(x)=x^3(x-6)^4 ?
The extreme f(x)=x^3(x-6)^4 is Saddle(0,0),Maximum(18/7 , 1934917632/823543),Minimum(6,0)