What is the extreme f(x)= 10/3 x^3-11x^2+12x-24 ?

The extreme f(x)= 10/3 x^3-11x^2+12x-24 is Maximum(1,-59/3),Minimum(6/5 ,-492/25)

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extreme f(x)= 10/3 x^3-11x^2+12x-24

extreme points

f (x) = \frac{10}{3} x^{3} - 11 x^{2} + 12 x - 24

Maximum (1, - \frac{59}{3}), Minimum (\frac{6}{5}, - \frac{492}{25})

Solution steps

f^{'} (x) = 10 x^{2} - 22 x + 12

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \frac{6}{5},

Increasing

: \frac{6}{5} < x < \infty

Plug

x = 1

into

\frac{10}{3} x^{3} - 11 x^{2} + 12 x - 24 : - \frac{59}{3}

Maximum (1, - \frac{59}{3})

Plug

x = \frac{6}{5}

into

\frac{10}{3} x^{3} - 11 x^{2} + 12 x - 24 : - \frac{492}{25}

Minimum (\frac{6}{5}, - \frac{492}{25})

Maximum (1, - \frac{59}{3}), Minimum (\frac{6}{5}, - \frac{492}{25})

What is the extreme f(x)= 10/3 x^3-11x^2+12x-24 ?
The extreme f(x)= 10/3 x^3-11x^2+12x-24 is Maximum(1,-59/3),Minimum(6/5 ,-492/25)