What is the extreme y=180x-0.3x^3 ?

The extreme y=180x-0.3x^3 is Minimum(-10sqrt(2),-1697.05627…),Maximum(10sqrt(2),1697.05627…)

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extreme y=180x-0.3x^3

extreme

Minimum (- 102, - 1697.05627 \dots), Maximum (102, 1697.05627 \dots)

Solution steps

f^{'} (x) = 180 - 0.9 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 102,

Increasing

: - 102 < x < 102,

Decreasing

: 102 < x < \infty

Plug

x = - 102

into

180 x - 0.3 x^{3} : - 1697.05627 \dots

Minimum (- 102, - 1697.05627 \dots)

Plug

x = 102

into

180 x - 0.3 x^{3} : 1697.05627 \dots

Maximum (102, 1697.05627 \dots)

Minimum (- 102, - 1697.05627 \dots), Maximum (102, 1697.05627 \dots)

What is the extreme y=180x-0.3x^3 ?
The extreme y=180x-0.3x^3 is Minimum(-10sqrt(2),-1697.05627…),Maximum(10sqrt(2),1697.05627…)