What is the extreme f(x)=x^4-20x^3+28x^2-4 ?

The extreme f(x)=x^4-20x^3+28x^2-4 is Minimum(0,-4),Maximum(1,5),Minimum(14,-10980)

Popular >

extreme f(x)=x^4-20x^3+28x^2-4

extreme points

f (x) = x^{4} - 20 x^{3} + 28 x^{2} - 4

Minimum (0, - 4), Maximum (1, 5), Minimum (14, - 10980)

Solution steps

f^{'} (x) = 4 x^{3} - 60 x^{2} + 56 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 14,

Increasing

: 14 < x < \infty

Plug

x = 0

into

x^{4} - 20 x^{3} + 28 x^{2} - 4 : - 4

Minimum (0, - 4)

Plug

x = 1

into

x^{4} - 20 x^{3} + 28 x^{2} - 4 : 5

Maximum (1, 5)

Plug

x = 14

into

x^{4} - 20 x^{3} + 28 x^{2} - 4 : - 10980

Minimum (14, - 10980)

Minimum (0, - 4), Maximum (1, 5), Minimum (14, - 10980)

1448.2 x^{2} - 81667 x + 1000000

f (x, y) = (x - 8)^{2} + (y - 5)^{2} + 16

f (x) = x e^{3 x^{2}}

f (x, y) = 2 x^{2} + y^{4} - 16 x y

f (x, y) = (7 x + 9 y + 8) e^{(- (x^{2} + y^{2}))}

What is the extreme f(x)=x^4-20x^3+28x^2-4 ?
The extreme f(x)=x^4-20x^3+28x^2-4 is Minimum(0,-4),Maximum(1,5),Minimum(14,-10980)