What is the extreme f(x)=-12x^5+135x^4-400x^3 ?

The extreme f(x)=-12x^5+135x^4-400x^3 is Saddle(0,0),Minimum(4,-3328),Maximum(5,-3125)

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extreme f(x)=-12x^5+135x^4-400x^3

extreme points

f (x) = - 12 x^{5} + 135 x^{4} - 400 x^{3}

Saddle (0, 0), Minimum (4, - 3328), Maximum (5, - 3125)

Solution steps

f^{'} (x) = - 60 x^{4} + 540 x^{3} - 1200 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = 0

into

- 12 x^{5} + 135 x^{4} - 400 x^{3} : 0

Saddle (0, 0)

Plug

x = 4

into

- 12 x^{5} + 135 x^{4} - 400 x^{3} : - 3328

Minimum (4, - 3328)

Plug

x = 5

into

- 12 x^{5} + 135 x^{4} - 400 x^{3} : - 3125

Maximum (5, - 3125)

Saddle (0, 0), Minimum (4, - 3328), Maximum (5, - 3125)

f (x) = 3 x^{5} - 45 x^{3}

x (x + 1) (x + 2) (x + 3)

y = x + 2 cos (x), 0 \leq x \leq 2 π

f (x, y) = y^{3} - x^{3} - 2 x y + 6

f (x) = x^{3} - 3 x^{2} - 9 x + 12

What is the extreme f(x)=-12x^5+135x^4-400x^3 ?
The extreme f(x)=-12x^5+135x^4-400x^3 is Saddle(0,0),Minimum(4,-3328),Maximum(5,-3125)