What is the extreme f(x)=3x^4-20x^3+24x^2 ?

The extreme f(x)=3x^4-20x^3+24x^2 is Minimum(0,0),Maximum(1,7),Minimum(4,-128)

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extreme f(x)=3x^4-20x^3+24x^2

extreme points

f (x) = 3 x^{4} - 20 x^{3} + 24 x^{2}

Minimum (0, 0), Maximum (1, 7), Minimum (4, - 128)

Solution steps

f^{'} (x) = 12 x^{3} - 60 x^{2} + 48 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

3 x^{4} - 20 x^{3} + 24 x^{2} : 0

Minimum (0, 0)

Plug

x = 1

into

3 x^{4} - 20 x^{3} + 24 x^{2} : 7

Maximum (1, 7)

Plug

x = 4

into

3 x^{4} - 20 x^{3} + 24 x^{2} : - 128

Minimum (4, - 128)

Minimum (0, 0), Maximum (1, 7), Minimum (4, - 128)

What is the extreme f(x)=3x^4-20x^3+24x^2 ?
The extreme f(x)=3x^4-20x^3+24x^2 is Minimum(0,0),Maximum(1,7),Minimum(4,-128)