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 points

f (t) = 108 t - t^{3}, - 7 \leq t < \infty

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)

f (x) = 2 ln (x) 1 + 3 ln (x) 2 + 3 ln (x) 3

f (x) = ln (x), 0 < x \leq 4

f (x, y) = e - (x^{2} + y^{2} - 6 y)

2 x^{3} + 6 x^{2} - 48 x

f (x) = - 2 x^{2} - 20 x + 8

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)