What is the extreme f(x)=-3x^4+24x^3-48x^2 ?

The extreme f(x)=-3x^4+24x^3-48x^2 is Maximum(0,0),Minimum(2,-48),Maximum(4,0)

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extreme f(x)=-3x^4+24x^3-48x^2

extreme points

f (x) = - 3 x^{4} + 24 x^{3} - 48 x^{2}

Maximum (0, 0), Minimum (2, - 48), Maximum (4, 0)

Solution steps

f^{'} (x) = - 12 x^{3} + 72 x^{2} - 96 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

- 3 x^{4} + 24 x^{3} - 48 x^{2} : 0

Maximum (0, 0)

Plug

x = 2

into

- 3 x^{4} + 24 x^{3} - 48 x^{2} : - 48

Minimum (2, - 48)

Plug

x = 4

into

- 3 x^{4} + 24 x^{3} - 48 x^{2} : 0

Maximum (4, 0)

Maximum (0, 0), Minimum (2, - 48), Maximum (4, 0)

f (x) = 3 x + 5 - 4

ln (tan (x)) - x^{2}

f (x) = 5 + (2 + x)^{\frac{1}{2}}

\frac{x - 2}{- x ^{2} - 2 x + 8}

x

What is the extreme f(x)=-3x^4+24x^3-48x^2 ?
The extreme f(x)=-3x^4+24x^3-48x^2 is Maximum(0,0),Minimum(2,-48),Maximum(4,0)