What is the extreme f(x)=8x^5-120x^3+43 ?

The extreme f(x)=8x^5-120x^3+43 is Maximum(-3,1339),Saddle(0,43),Minimum(3,-1253)

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extreme f(x)=8x^5-120x^3+43

extreme points

f (x) = 8 x^{5} - 120 x^{3} + 43

Maximum (- 3, 1339), Saddle (0, 43), Minimum (3, - 1253)

Solution steps

f^{'} (x) = 40 x^{4} - 360 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

8 x^{5} - 120 x^{3} + 43 : 1339

Maximum (- 3, 1339)

Plug

x = 0

into

8 x^{5} - 120 x^{3} + 43 : 43

Saddle (0, 43)

Plug

x = 3

into

8 x^{5} - 120 x^{3} + 43 : - 1253

Minimum (3, - 1253)

Maximum (- 3, 1339), Saddle (0, 43), Minimum (3, - 1253)

f (x) = \frac{x ^{2}}{x ^{4} + 1}

f (x) = (8 x)^{3} - (5 x)^{2} - 3 x

f (x) = 2

f (x, y) = 3 x^{3} + x y^{2} - 2 x y + 1

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

What is the extreme f(x)=8x^5-120x^3+43 ?
The extreme f(x)=8x^5-120x^3+43 is Maximum(-3,1339),Saddle(0,43),Minimum(3,-1253)