What is the extreme f(x)=2x^3-3x+10 ?

The extreme f(x)=2x^3-3x+10 is Maximum(-1/(sqrt(2)),sqrt(2)+10),Minimum(1/(sqrt(2)),-sqrt(2)+10)

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extreme f(x)=2x^3-3x+10

extreme points

f (x) = 2 x^{3} - 3 x + 10

Maximum (- \frac{1}{2}, 2 + 10), Minimum (\frac{1}{2}, - 2 + 10)

Solution steps

f^{'} (x) = 6 x^{2} - 3

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

2 x^{3} - 3 x + 10 : 2 + 10

Maximum (- \frac{1}{2}, 2 + 10)

Plug

x = \frac{1}{2}

into

2 x^{3} - 3 x + 10 : - 2 + 10

Minimum (\frac{1}{2}, - 2 + 10)

Maximum (- \frac{1}{2}, 2 + 10), Minimum (\frac{1}{2}, - 2 + 10)

What is the extreme f(x)=2x^3-3x+10 ?
The extreme f(x)=2x^3-3x+10 is Maximum(-1/(sqrt(2)),sqrt(2)+10),Minimum(1/(sqrt(2)),-sqrt(2)+10)