What is the extreme x^4-5x^3+x^2+21x-18 ?

The extreme x^4-5x^3+x^2+21x-18 is Minimum(-1,-32),Maximum(7/4 , 1125/256),Minimum(3,0)

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extreme x^4-5x^3+x^2+21x-18

extreme points

x^{4} - 5 x^{3} + x^{2} + 21 x - 18

Minimum (- 1, - 32), Maximum (\frac{7}{4}, \frac{1125}{256}), Minimum (3, 0)

Solution steps

f^{'} (x) = 4 x^{3} - 15 x^{2} + 2 x + 21

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < \frac{7}{4},

Decreasing

: \frac{7}{4} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

x^{4} - 5 x^{3} + x^{2} + 21 x - 18 : - 32

Minimum (- 1, - 32)

Plug

x = \frac{7}{4}

into

x^{4} - 5 x^{3} + x^{2} + 21 x - 18 : \frac{1125}{256}

Maximum (\frac{7}{4}, \frac{1125}{256})

Plug

x = 3

into

x^{4} - 5 x^{3} + x^{2} + 21 x - 18 : 0

Minimum (3, 0)

Minimum (- 1, - 32), Maximum (\frac{7}{4}, \frac{1125}{256}), Minimum (3, 0)

x^{2} + 64

x^{3} - 3 x^{2} - 9 x + 9

f (x) = x (x - 9)^{2}

f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 60

f (x) = \frac{x ( x - 4 ) ^{2}}{4}

What is the extreme x^4-5x^3+x^2+21x-18 ?
The extreme x^4-5x^3+x^2+21x-18 is Minimum(-1,-32),Maximum(7/4 , 1125/256),Minimum(3,0)