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

The extreme f(x)=x^4(x-3)^3 is Maximum(0,0),Minimum(12/7 ,-15116544/823543),Saddle(3,0)

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

extreme

Maximum (0, 0), Minimum (\frac{12}{7}, - \frac{15116544}{823543}), Saddle (3, 0)

Solution steps

f^{'} (x) = x^{3} (x - 3)^{2} (7 x - 12)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{12}{7},

Increasing

: \frac{12}{7} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{12}{7}

into

x^{4} (x - 3)^{3} : - \frac{15116544}{823543}

Minimum (\frac{12}{7}, - \frac{15116544}{823543})

Plug

x = 3

into

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

Saddle (3, 0)

Maximum (0, 0), Minimum (\frac{12}{7}, - \frac{15116544}{823543}), Saddle (3, 0)

What is the extreme f(x)=x^4(x-3)^3 ?
The extreme f(x)=x^4(x-3)^3 is Maximum(0,0),Minimum(12/7 ,-15116544/823543),Saddle(3,0)