What is the extreme f(x)=x^4-14x^2-24x+1 ?

The extreme f(x)=x^4-14x^2-24x+1 is Minimum(-2,9),Maximum(-1,12),Minimum(3,-116)

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extreme f(x)=x^4-14x^2-24x+1

extreme points

f (x) = x^{4} - 14 x^{2} - 24 x + 1

Minimum (- 2, 9), Maximum (- 1, 12), Minimum (3, - 116)

Solution steps

f^{'} (x) = 4 x^{3} - 28 x - 24

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < - 1,

Decreasing

: - 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

x^{4} - 14 x^{2} - 24 x + 1 : 9

Minimum (- 2, 9)

Plug

x = - 1

into

x^{4} - 14 x^{2} - 24 x + 1 : 12

Maximum (- 1, 12)

Plug

x = 3

into

x^{4} - 14 x^{2} - 24 x + 1 : - 116

Minimum (3, - 116)

Minimum (- 2, 9), Maximum (- 1, 12), Minimum (3, - 116)

f (x, y) = x^{2} y + 2 x y^{2} - 8 x + 4

f (x) = x^{4} - 8 x^{2} + 5

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

f (x, y) = \frac{1}{x + y}

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

What is the extreme f(x)=x^4-14x^2-24x+1 ?
The extreme f(x)=x^4-14x^2-24x+1 is Minimum(-2,9),Maximum(-1,12),Minimum(3,-116)