What is the extreme f(t)=108t-t^3,-7<= t<infinity ?

The extreme f(t)=108t-t^3,-7<= t<infinity is Maximum(-7,-413),Minimum(-6,-432),Maximum(6,432)

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extreme f(t)=108t-t^3,-7<= t<infinity

extreme

Maximum (- 7, - 413), Minimum (- 6, - 432), Maximum (6, 432)

Solution steps

Find the critical points:

t = - 7, t = - 6, t = 6

Domain of

108 t - t^{3}, - 7 \leq t < \infty : t \geq - 7

Find intervals:

Decreasing

: - 7 < t < - 6,

Increasing

: - 6 < t < 6,

Decreasing

: 6 < t < \infty

Plug the extreme point

x = - 7

into

108 t - t^{3} \Rightarrow y = - 413

Maximum (- 7, - 413)

Plug the extreme point

x = - 6

into

108 t - t^{3} \Rightarrow y = - 432

Minimum (- 6, - 432)

Plug the extreme point

x = 6

into

108 t - t^{3} \Rightarrow y = 432

Maximum (6, 432)

Maximum (- 7, - 413), Minimum (- 6, - 432), Maximum (6, 432)

What is the extreme f(t)=108t-t^3,-7<= t<infinity ?
The extreme f(t)=108t-t^3,-7<= t<infinity is Maximum(-7,-413),Minimum(-6,-432),Maximum(6,432)