What is the extreme f(x)=x^3-6x^2-63x+6 ?

The extreme f(x)=x^3-6x^2-63x+6 is Maximum(-3,114),Minimum(7,-386)

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extreme f(x)=x^3-6x^2-63x+6

extreme points

f (x) = x^{3} - 6 x^{2} - 63 x + 6

Maximum (- 3, 114), Minimum (7, - 386)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x - 63

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 7,

Increasing

: 7 < x < \infty

Plug

x = - 3

into

x^{3} - 6 x^{2} - 63 x + 6 : 114

Maximum (- 3, 114)

Plug

x = 7

into

x^{3} - 6 x^{2} - 63 x + 6 : - 386

Minimum (7, - 386)

Maximum (- 3, 114), Minimum (7, - 386)

y = x e^{x}

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

f (x, y) = (6 x - x^{2}) (4 y - y^{2})

ln (x) - 3 x + 2

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

What is the extreme f(x)=x^3-6x^2-63x+6 ?
The extreme f(x)=x^3-6x^2-63x+6 is Maximum(-3,114),Minimum(7,-386)