What is the extreme f(x)=x^3-3x[0.3] ?

The extreme f(x)=x^3-3x[0.3] is Maximum(-sqrt(3/10),0.32863…),Minimum(sqrt(3/10),-0.32863…)

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extreme f(x)=x^3-3x[0.3]

extreme

Maximum (- \frac{3}{10}, 0.32863 \dots), Minimum (\frac{3}{10}, - 0.32863 \dots)

Solution steps

f^{'} (x) = 3 x^{2} - 0.9

Find intervals:

Increasing

: - \infty < x < - 0.54772 \dots,

Decreasing

: - 0.54772 \dots < x < 0.54772 \dots,

Increasing

: 0.54772 \dots < x < \infty

Plug

x = - \frac{3}{10}

into

x^{3} - 3 x [0.3] : 0.32863 \dots

Maximum (- \frac{3}{10}, 0.32863 \dots)

Plug

x = \frac{3}{10}

into

x^{3} - 3 x [0.3] : - 0.32863 \dots

Minimum (\frac{3}{10}, - 0.32863 \dots)

Maximum (- \frac{3}{10}, 0.32863 \dots), Minimum (\frac{3}{10}, - 0.32863 \dots)

What is the extreme f(x)=x^3-3x[0.3] ?
The extreme f(x)=x^3-3x[0.3] is Maximum(-sqrt(3/10),0.32863…),Minimum(sqrt(3/10),-0.32863…)