What is the extreme f(x)=12x^5+45x^4-360x^3+6 ?

The extreme f(x)=12x^5+45x^4-360x^3+6 is Maximum(-6,42774),Saddle(0,6),Minimum(3,-3153)

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extreme f(x)=12x^5+45x^4-360x^3+6

extreme

Maximum (- 6, 42774), Saddle (0, 6), Minimum (3, - 3153)

Solution steps

f^{'} (x) = 60 x^{4} + 180 x^{3} - 1080 x^{2}

Find intervals:

Increasing

: - \infty < x < - 6,

Decreasing

: - 6 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 6

into

12 x^{5} + 45 x^{4} - 360 x^{3} + 6 : 42774

Maximum (- 6, 42774)

Plug

x = 0

into

12 x^{5} + 45 x^{4} - 360 x^{3} + 6 : 6

Saddle (0, 6)

Plug

x = 3

into

12 x^{5} + 45 x^{4} - 360 x^{3} + 6 : - 3153

Minimum (3, - 3153)

Maximum (- 6, 42774), Saddle (0, 6), Minimum (3, - 3153)

What is the extreme f(x)=12x^5+45x^4-360x^3+6 ?
The extreme f(x)=12x^5+45x^4-360x^3+6 is Maximum(-6,42774),Saddle(0,6),Minimum(3,-3153)