What is the extreme 7x^5-105x^3 ?

The extreme 7x^5-105x^3 is Maximum(-3,1134),Saddle(0,0),Minimum(3,-1134)

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extreme 7x^5-105x^3

extreme points

7 x^{5} - 105 x^{3}

Maximum (- 3, 1134), Saddle (0, 0), Minimum (3, - 1134)

Solution steps

f^{'} (x) = 35 x^{4} - 315 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

7 x^{5} - 105 x^{3} : 1134

Maximum (- 3, 1134)

Plug

x = 0

into

7 x^{5} - 105 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

7 x^{5} - 105 x^{3} : - 1134

Minimum (3, - 1134)

Maximum (- 3, 1134), Saddle (0, 0), Minimum (3, - 1134)

f (x) = x^{3} - 9 x^{2} + 15 x + 7

f (x) = \frac{6 x - 1}{x}

f (x) = x^{2} \cdot (2 - x)^{2}

f (x, y) = 4 x^{2} - 8 x + 5 y^{2} + 6

- (x^{2} - y^{2}) e^{- x^{2} - y^{2}}

What is the extreme 7x^5-105x^3 ?
The extreme 7x^5-105x^3 is Maximum(-3,1134),Saddle(0,0),Minimum(3,-1134)