What is the extreme f(x)=x^4-24x^2+23 ?

The extreme f(x)=x^4-24x^2+23 is Minimum(-2sqrt(3),-121),Maximum(0,23),Minimum(2sqrt(3),-121)

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extreme f(x)=x^4-24x^2+23

extreme points

f (x) = x^{4} - 24 x^{2} + 23

Minimum (- 23, - 121), Maximum (0, 23), Minimum (23, - 121)

Solution steps

f^{'} (x) = 4 x^{3} - 48 x

Find intervals:

Decreasing

: - \infty < x < - 23,

Increasing

: - 23 < x < 0,

Decreasing

: 0 < x < 23,

Increasing

: 23 < x < \infty

Plug

x = - 23

into

x^{4} - 24 x^{2} + 23 : - 121

Minimum (- 23, - 121)

Plug

x = 0

into

x^{4} - 24 x^{2} + 23 : 23

Maximum (0, 23)

Plug

x = 23

into

x^{4} - 24 x^{2} + 23 : - 121

Minimum (23, - 121)

Minimum (- 23, - 121), Maximum (0, 23), Minimum (23, - 121)

\frac{( x ^{2} - 5 ) ^{3}}{125}

f (x) = 2 x^{2} - 6 x + 4, 0 \leq x \leq 10

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

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

f (x) = \frac{4 x + 3}{x ^{2}}

What is the extreme f(x)=x^4-24x^2+23 ?
The extreme f(x)=x^4-24x^2+23 is Minimum(-2sqrt(3),-121),Maximum(0,23),Minimum(2sqrt(3),-121)