What is the extreme f(x)=x^3-9/2 x^2-54x+12 ?

The extreme f(x)=x^3-9/2 x^2-54x+12 is Maximum(-3, 213/2),Minimum(6,-258)

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extreme f(x)=x^3-9/2 x^2-54x+12

extreme points

f (x) = x^{3} - \frac{9}{2} x^{2} - 54 x + 12

Maximum (- 3, \frac{213}{2}), Minimum (6, - 258)

Solution steps

f^{'} (x) = 3 x^{2} - 9 x - 54

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 3

into

x^{3} - \frac{9}{2} x^{2} - 54 x + 12 : \frac{213}{2}

Maximum (- 3, \frac{213}{2})

Plug

x = 6

into

x^{3} - \frac{9}{2} x^{2} - 54 x + 12 : - 258

Minimum (6, - 258)

Maximum (- 3, \frac{213}{2}), Minimum (6, - 258)

f (x) = x^{2} - 6 x^{2} + 1

y = x^{2} - 3 x - 70

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

- x^{3} + 3 x^{2} + 9

f (x) = x^{2} + y^{2} + 6 x - 12 y - 9

What is the extreme f(x)=x^3-9/2 x^2-54x+12 ?
The extreme f(x)=x^3-9/2 x^2-54x+12 is Maximum(-3, 213/2),Minimum(6,-258)