What is the extreme f(x)=x^4+4x^3-20x^2+1 ?

The extreme f(x)=x^4+4x^3-20x^2+1 is Minimum(-5,-374),Maximum(0,1),Minimum(2,-31)

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extreme f(x)=x^4+4x^3-20x^2+1

extreme points

f (x) = x^{4} + 4 x^{3} - 20 x^{2} + 1

Minimum (- 5, - 374), Maximum (0, 1), Minimum (2, - 31)

Solution steps

f^{'} (x) = 4 x^{3} + 12 x^{2} - 40 x

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 5

into

x^{4} + 4 x^{3} - 20 x^{2} + 1 : - 374

Minimum (- 5, - 374)

Plug

x = 0

into

x^{4} + 4 x^{3} - 20 x^{2} + 1 : 1

Maximum (0, 1)

Plug

x = 2

into

x^{4} + 4 x^{3} - 20 x^{2} + 1 : - 31

Minimum (2, - 31)

Minimum (- 5, - 374), Maximum (0, 1), Minimum (2, - 31)

f (x) = e^{\frac{x}{2}} (x + y^{2})

f (x) = x^{4} - 50 x^{2} + 1

f (x) = x^{4} - 50 x^{2} + 2

y = x^{3} - 3 x^{2} + 5

+ \frac{x}{x ^{2} - 25}

What is the extreme f(x)=x^4+4x^3-20x^2+1 ?
The extreme f(x)=x^4+4x^3-20x^2+1 is Minimum(-5,-374),Maximum(0,1),Minimum(2,-31)