What is the extreme f(x)=3x^3+9/2 x^2-54x+1 ?

The extreme f(x)=3x^3+9/2 x^2-54x+1 is Maximum(-3, 245/2),Minimum(2,-65)

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extreme f(x)=3x^3+9/2 x^2-54x+1

extreme points

f (x) = 3 x^{3} + \frac{9}{2} x^{2} - 54 x + 1

Maximum (- 3, \frac{245}{2}), Minimum (2, - 65)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 3

into

3 x^{3} + \frac{9}{2} x^{2} - 54 x + 1 : \frac{245}{2}

Maximum (- 3, \frac{245}{2})

Plug

x = 2

into

3 x^{3} + \frac{9}{2} x^{2} - 54 x + 1 : - 65

Minimum (2, - 65)

Maximum (- 3, \frac{245}{2}), Minimum (2, - 65)

f (x) = (1 - x)^{2} \cdot (1 + x)^{3}

f (x) = \frac{x ^{4} - 5 x + 7}{x ^{2} + 1}

f (x) = 5 - 6 x^{2}

y = \frac{- 8 - 8 x ^{2}}{2 x ( 1 + x )}

f (t) = \frac{e ^{t}}{t ^{2} + 1}

What is the extreme f(x)=3x^3+9/2 x^2-54x+1 ?
The extreme f(x)=3x^3+9/2 x^2-54x+1 is Maximum(-3, 245/2),Minimum(2,-65)