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Popular >

extreme f(x)=7x^9-9x^7-7,-3<= x<= 3

Solution

extreme points

f (x) = 7 x^{9} - 9 x^{7} - 7, - 3 \leq x \leq 3

Solution

Minimum (- 3, - 118105), Maximum (- 1, - 5), Saddle (0, - 7), Minimum (1, - 9), Maximum (3, 118091)

Solution steps

Find the critical points:

x = - 3, x = - 1, x = 0, x = 1, x = 3

Domain of

7 x^{9} - 9 x^{7} - 7, - 3 \leq x \leq 3 : - 3 \leq x \leq 3

Find intervals:

Increasing

: - 3 < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < 3

Plug the extreme point

x = - 3

into

7 x^{9} - 9 x^{7} - 7 \Rightarrow y = - 118105

Minimum (- 3, - 118105)

Plug the extreme point

x = - 1

into

7 x^{9} - 9 x^{7} - 7 \Rightarrow y = - 5

Maximum (- 1, - 5)

Plug the extreme point

x = 0

into

7 x^{9} - 9 x^{7} - 7 \Rightarrow y = - 7

Saddle (0, - 7)

Plug the extreme point

x = 1

into

7 x^{9} - 9 x^{7} - 7 \Rightarrow y = - 9

Minimum (1, - 9)

Plug the extreme point

x = 3

into

7 x^{9} - 9 x^{7} - 7 \Rightarrow y = 118091

Maximum (3, 118091)

Minimum (- 3, - 118105), Maximum (- 1, - 5), Saddle (0, - 7), Minimum (1, - 9), Maximum (3, 118091)

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