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

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 1

into

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

Minimum (1, - 7)

Plug

x = 4

into

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

Maximum (4, 128)

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

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

\frac{8 x}{x + 5}

f (x) = \frac{1}{6} x^{2} - 1

\frac{14 x}{x + 14}

\frac{2 x - 4}{x ^{2} + x - 2}

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