What is the extreme f(x)=2x^3-13x^2+24x-28 ?

The extreme f(x)=2x^3-13x^2+24x-28 is Maximum(4/3 ,-388/27),Minimum(3,-19)

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extreme f(x)=2x^3-13x^2+24x-28

extreme points

f (x) = 2 x^{3} - 13 x^{2} + 24 x - 28

Maximum (\frac{4}{3}, - \frac{388}{27}), Minimum (3, - 19)

Solution steps

f^{'} (x) = 6 x^{2} - 26 x + 24

Find intervals:

Increasing

: - \infty < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = \frac{4}{3}

into

2 x^{3} - 13 x^{2} + 24 x - 28 : - \frac{388}{27}

Maximum (\frac{4}{3}, - \frac{388}{27})

Plug

x = 3

into

2 x^{3} - 13 x^{2} + 24 x - 28 : - 19

Minimum (3, - 19)

Maximum (\frac{4}{3}, - \frac{388}{27}), Minimum (3, - 19)

What is the extreme f(x)=2x^3-13x^2+24x-28 ?
The extreme f(x)=2x^3-13x^2+24x-28 is Maximum(4/3 ,-388/27),Minimum(3,-19)