What is the extreme f(x)=x^{6/7},-2<= x<= 4 ?

The extreme f(x)=x^{6/7},-2<= x<= 4 is Maximum(-2,(-2)^{6/7}),Minimum(0,0),Maximum(4,4^{6/7})

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extreme f(x)=x^{6/7},-2<= x<= 4

extreme

Maximum (- 2, (- 2)^{\frac{6}{7}}), Minimum (0, 0), Maximum (4, 4^{\frac{6}{7}})

Solution steps

Find the critical points:

x = - 2, x = 0, x = 4

Domain of

x^{\frac{6}{7}}, - 2 \leq x \leq 4 : - 2 \leq x \leq 4

Find intervals:

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 4

Plug the extreme point

x = - 2

into

x^{\frac{6}{7}} \Rightarrow y = (- 2)^{\frac{6}{7}}

Maximum (- 2, (- 2)^{\frac{6}{7}})

Plug the extreme point

x = 0

into

x^{\frac{6}{7}} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 4

into

x^{\frac{6}{7}} \Rightarrow y = 4^{\frac{6}{7}}

Maximum (4, 4^{\frac{6}{7}})

Maximum (- 2, (- 2)^{\frac{6}{7}}), Minimum (0, 0), Maximum (4, 4^{\frac{6}{7}})

What is the extreme f(x)=x^{6/7},-2<= x<= 4 ?
The extreme f(x)=x^{6/7},-2<= x<= 4 is Maximum(-2,(-2)^{6/7}),Minimum(0,0),Maximum(4,4^{6/7})