What is the extreme f(x)=4x^5-25x^4+40x^3-4[-1.4] ?

The extreme f(x)=4x^5-25x^4+40x^3-4[-1.4] is Saddle(0,5.6),Maximum(2,53.6),Minimum(3,32.6)

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extreme f(x)=4x^5-25x^4+40x^3-4[-1.4]

extreme points

f (x) = 4 x^{5} - 25 x^{4} + 40 x^{3} - 4 [- 1.4]

Saddle (0, 5.6), Maximum (2, 53.6), Minimum (3, 32.6)

Solution steps

f^{'} (x) = 20 x^{4} - 100 x^{3} + 120 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

4 x^{5} - 25 x^{4} + 40 x^{3} - 4 [- 1.4] : 5.6

Saddle (0, 5.6)

Plug

x = 2

into

4 x^{5} - 25 x^{4} + 40 x^{3} - 4 [- 1.4] : 53.6

Maximum (2, 53.6)

Plug

x = 3

into

4 x^{5} - 25 x^{4} + 40 x^{3} - 4 [- 1.4] : 32.6

Minimum (3, 32.6)

Saddle (0, 5.6), Maximum (2, 53.6), Minimum (3, 32.6)

f (x) = - \frac{1}{2} x^{2} + 15 x - 51

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

f (x) = x^{2} + y^{2} - 16 = 0

2 x^{2} - 2 x^{2} y + y^{2}

x^{2} + x + 2

What is the extreme f(x)=4x^5-25x^4+40x^3-4[-1.4] ?
The extreme f(x)=4x^5-25x^4+40x^3-4[-1.4] is Saddle(0,5.6),Maximum(2,53.6),Minimum(3,32.6)