What is the extreme f(t)=135t-5t^3,-4<= t<= infinity ?

The extreme f(t)=135t-5t^3,-4<= t<= infinity is Maximum(-4,-220),Minimum(-3,-270),Maximum(3,270)

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extreme f(t)=135t-5t^3,-4<= t<= infinity

extreme points

f (t) = 135 t - 5 t^{3}, - 4 \leq t \leq \infty

Maximum (- 4, - 220), Minimum (- 3, - 270), Maximum (3, 270)

Solution steps

Find the critical points:

t = - 4, t = - 3, t = 3

Domain of

135 t - 5 t^{3}, - 4 \leq t \leq \infty : t \geq - 4

Find intervals:

Decreasing

: - 4 < t < - 3,

Increasing

: - 3 < t < 3,

Decreasing

: 3 < t < \infty

Plug the extreme point

x = - 4

into

135 t - 5 t^{3} \Rightarrow y = - 220

Maximum (- 4, - 220)

Plug the extreme point

x = - 3

into

135 t - 5 t^{3} \Rightarrow y = - 270

Minimum (- 3, - 270)

Plug the extreme point

x = 3

into

135 t - 5 t^{3} \Rightarrow y = 270

Maximum (3, 270)

Maximum (- 4, - 220), Minimum (- 3, - 270), Maximum (3, 270)

f (x) = 2 x^{3} - 4 x + 4

P (x, y) = 2 x + y

y = \frac{5280}{π x ^{2}} - \frac{4}{3} x

x^{3} - 6 x^{2} - 15 x + 2

x^{3} - 6 x^{2} - 15 x + 4

What is the extreme f(t)=135t-5t^3,-4<= t<= infinity ?
The extreme f(t)=135t-5t^3,-4<= t<= infinity is Maximum(-4,-220),Minimum(-3,-270),Maximum(3,270)