What is the extreme f(x)=-3x^4+24x^3-30x^2 ?

The extreme f(x)=-3x^4+24x^3-30x^2 is Maximum(0,0),Minimum(1,-9),Maximum(5,375)

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extreme f(x)=-3x^4+24x^3-30x^2

extreme points

f (x) = - 3 x^{4} + 24 x^{3} - 30 x^{2}

Maximum (0, 0), Minimum (1, - 9), Maximum (5, 375)

Solution steps

f^{'} (x) = - 12 x^{3} + 72 x^{2} - 60 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = 0

into

- 3 x^{4} + 24 x^{3} - 30 x^{2} : 0

Maximum (0, 0)

Plug

x = 1

into

- 3 x^{4} + 24 x^{3} - 30 x^{2} : - 9

Minimum (1, - 9)

Plug

x = 5

into

- 3 x^{4} + 24 x^{3} - 30 x^{2} : 375

Maximum (5, 375)

Maximum (0, 0), Minimum (1, - 9), Maximum (5, 375)

f (x) = 3 lo g_{2} (2 x - 8)

f (x) = - tan (\frac{1}{4} x)

y = cos (3 x)

f (x) = (x - 4)^{2} - 1

f (x) = - 35 x + 5

What is the extreme f(x)=-3x^4+24x^3-30x^2 ?
The extreme f(x)=-3x^4+24x^3-30x^2 is Maximum(0,0),Minimum(1,-9),Maximum(5,375)