What is the extreme f(x)=48x^3+57x^2-54x+18 ?

The extreme f(x)=48x^3+57x^2-54x+18 is Maximum(-9/8 , 5283/64),Minimum(1/3 , 73/9)

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extreme f(x)=48x^3+57x^2-54x+18

extreme points

f (x) = 48 x^{3} + 57 x^{2} - 54 x + 18

Maximum (- \frac{9}{8}, \frac{5283}{64}), Minimum (\frac{1}{3}, \frac{73}{9})

Solution steps

f^{'} (x) = 144 x^{2} + 114 x - 54

Find intervals:

Increasing

: - \infty < x < - \frac{9}{8},

Decreasing

: - \frac{9}{8} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - \frac{9}{8}

into

48 x^{3} + 57 x^{2} - 54 x + 18 : \frac{5283}{64}

Maximum (- \frac{9}{8}, \frac{5283}{64})

Plug

x = \frac{1}{3}

into

48 x^{3} + 57 x^{2} - 54 x + 18 : \frac{73}{9}

Minimum (\frac{1}{3}, \frac{73}{9})

Maximum (- \frac{9}{8}, \frac{5283}{64}), Minimum (\frac{1}{3}, \frac{73}{9})

f (x y) = x^{3} + y^{3} - 3 x y

f (x) = \frac{x ^{2} + 3}{x ^{2} - 16}

3 x^{4} + 3 y^{4} - x y

f (x) = \frac{x ^{2} - 1}{x - 1}

f (x) = x^{2} + y^{2} + x y

What is the extreme f(x)=48x^3+57x^2-54x+18 ?
The extreme f(x)=48x^3+57x^2-54x+18 is Maximum(-9/8 , 5283/64),Minimum(1/3 , 73/9)