What is the extreme f(x)=-3x^4+20x^3-36x^2+7 ?

The extreme f(x)=-3x^4+20x^3-36x^2+7 is Maximum(0,7),Minimum(2,-25),Maximum(3,-20)

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extreme f(x)=-3x^4+20x^3-36x^2+7

extreme points

f (x) = - 3 x^{4} + 20 x^{3} - 36 x^{2} + 7

Maximum (0, 7), Minimum (2, - 25), Maximum (3, - 20)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

- 3 x^{4} + 20 x^{3} - 36 x^{2} + 7 : 7

Maximum (0, 7)

Plug

x = 2

into

- 3 x^{4} + 20 x^{3} - 36 x^{2} + 7 : - 25

Minimum (2, - 25)

Plug

x = 3

into

- 3 x^{4} + 20 x^{3} - 36 x^{2} + 7 : - 20

Maximum (3, - 20)

Maximum (0, 7), Minimum (2, - 25), Maximum (3, - 20)

y = - 2 + 5 sin (\frac{π}{12} (x - 2))

(x^{2} - 1) (x^{2} - 9)

f (x) = 3 x^{2} + 2 y^{2} - x y - 4 x - 7 y + 12

y = \frac{\frac{25}{32} x ^{3} + 6400}{x}

f (x) = x ∣ x ∣

What is the extreme f(x)=-3x^4+20x^3-36x^2+7 ?
The extreme f(x)=-3x^4+20x^3-36x^2+7 is Maximum(0,7),Minimum(2,-25),Maximum(3,-20)