What is the extreme f(x)=5x^7-7x^5-7 ?

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

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extreme f(x)=5x^7-7x^5-7

extreme points

f (x) = 5 x^{7} - 7 x^{5} - 7

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

Solution steps

f^{'} (x) = 35 x^{6} - 35 x^{4}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, - 5)

Plug

x = 0

into

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

Saddle (0, - 7)

Plug

x = 1

into

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

Minimum (1, - 9)

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

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