What is the extreme f(x)=x^4-98x^2-1,(-8,8) ?

The extreme f(x)=x^4-98x^2-1,(-8,8) is Minimum(-7,-2402),Maximum(0,-1),Minimum(7,-2402)

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extreme f(x)=x^4-98x^2-1,(-8,8)

extreme points

f (x) = x^{4} - 98 x^{2} - 1, (- 8, 8)

Minimum (- 7, - 2402), Maximum (0, - 1), Minimum (7, - 2402)

Solution steps

Find the critical points:

x = - 7, x = 0, x = 7

Domain of

x^{4} - 98 x^{2} - 1, (- 8, 8) : - 8 < x < 8

Find intervals:

Decreasing

: - 8 < x < - 7,

Increasing

: - 7 < x < 0,

Decreasing

: 0 < x < 7,

Increasing

: 7 < x < 8

Plug the extreme point

x = - 7

into

x^{4} - 98 x^{2} - 1 \Rightarrow y = - 2402

Minimum (- 7, - 2402)

Plug the extreme point

x = 0

into

x^{4} - 98 x^{2} - 1 \Rightarrow y = - 1

Maximum (0, - 1)

Plug the extreme point

x = 7

into

x^{4} - 98 x^{2} - 1 \Rightarrow y = - 2402

Minimum (7, - 2402)

Minimum (- 7, - 2402), Maximum (0, - 1), Minimum (7, - 2402)

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

5 x + \frac{100}{x}

f (x) = 3 x^{3} - 9 x^{2} - 315 x + 7

f (x) = \frac{2 x ^{2}}{x - 2}, (- 2, 1)

f (x) = 250 (0.9)^{x}, 0 \leq x \leq 6

What is the extreme f(x)=x^4-98x^2-1,(-8,8) ?
The extreme f(x)=x^4-98x^2-1,(-8,8) is Minimum(-7,-2402),Maximum(0,-1),Minimum(7,-2402)