What is the extreme f(x)=x^3-4.5x^2-12x-2 ?

The extreme f(x)=x^3-4.5x^2-12x-2 is Maximum(-1,4.5),Minimum(4,-58)

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extreme f(x)=x^3-4.5x^2-12x-2

extreme points

f (x) = x^{3} - 4.5 x^{2} - 12 x - 2

Maximum (- 1, 4.5), Minimum (4, - 58)

Solution steps

f^{'} (x) = 3 x^{2} - 9 x - 12

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 1

into

x^{3} - 4.5 x^{2} - 12 x - 2 : 4.5

Maximum (- 1, 4.5)

Plug

x = 4

into

x^{3} - 4.5 x^{2} - 12 x - 2 : - 58

Minimum (4, - 58)

Maximum (- 1, 4.5), Minimum (4, - 58)

f (t) = 3 t + \frac{1}{t}

f (x) = \frac{9}{2} x^{2} - ln (x)

f (x) = 3 x + 1

f (x) = \frac{5 ( x - 6 ) ^{2}}{x - 1}

f (x) = x^{2} + 4 x y + y^{2}

What is the extreme f(x)=x^3-4.5x^2-12x-2 ?
The extreme f(x)=x^3-4.5x^2-12x-2 is Maximum(-1,4.5),Minimum(4,-58)