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

The extreme 3x^5-5x^3-7 is Maximum(-1,-5),Saddle(0,-7),Minimum(1,-9)

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extreme 3x^5-5x^3-7

extreme points

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

Maximum (- 1, - 5), Saddle (0, - 7), Minimum (1, - 9)

Solution steps

f^{'} (x) = 15 x^{4} - 15 x^{2}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, - 5)

Plug

x = 0

into

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

Saddle (0, - 7)

Plug

x = 1

into

3 x^{5} - 5 x^{3} - 7 : - 9

Minimum (1, - 9)

Maximum (- 1, - 5), Saddle (0, - 7), Minimum (1, - 9)

\frac{x + 1}{x}

(1, - 7), (2, - 1)

f (x) = x^{2} + 4 x

y = \frac{1}{8} x + 2

f (x) = 3 x^{2} - 12 x + 8

What is the extreme 3x^5-5x^3-7 ?
The extreme 3x^5-5x^3-7 is Maximum(-1,-5),Saddle(0,-7),Minimum(1,-9)