What is the extreme f(x)= 1/4 x^4-x,-4<= x<= 4 ?

The extreme f(x)= 1/4 x^4-x,-4<= x<= 4 is Maximum(-4,68),Minimum(1,-3/4),Maximum(4,60)

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extreme f(x)= 1/4 x^4-x,-4<= x<= 4

extreme

Maximum (- 4, 68), Minimum (1, - \frac{3}{4}), Maximum (4, 60)

Solution steps

Find the critical points:

x = - 4, x = 1, x = 4

Domain of

\frac{1}{4} x^{4} - x, - 4 \leq x \leq 4 : - 4 \leq x \leq 4

Find intervals:

Decreasing

: - 4 < x < 1,

Increasing

: 1 < x < 4

Plug the extreme point

x = - 4

into

\frac{1}{4} x^{4} - x \Rightarrow y = 68

Maximum (- 4, 68)

Plug the extreme point

x = 1

into

\frac{1}{4} x^{4} - x \Rightarrow y = - \frac{3}{4}

Minimum (1, - \frac{3}{4})

Plug the extreme point

x = 4

into

\frac{1}{4} x^{4} - x \Rightarrow y = 60

Maximum (4, 60)

Maximum (- 4, 68), Minimum (1, - \frac{3}{4}), Maximum (4, 60)

What is the extreme f(x)= 1/4 x^4-x,-4<= x<= 4 ?
The extreme f(x)= 1/4 x^4-x,-4<= x<= 4 is Maximum(-4,68),Minimum(1,-3/4),Maximum(4,60)