What is the extreme x^3-3x^2-24x+8 ?

The extreme x^3-3x^2-24x+8 is Maximum(-2,36),Minimum(4,-72)

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extreme x^3-3x^2-24x+8

extreme points

x^{3} - 3 x^{2} - 24 x + 8

Maximum (- 2, 36), Minimum (4, - 72)

Solution steps

f^{'} (x) = 3 x^{2} - 6 x - 24

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 2

into

x^{3} - 3 x^{2} - 24 x + 8 : 36

Maximum (- 2, 36)

Plug

x = 4

into

x^{3} - 3 x^{2} - 24 x + 8 : - 72

Minimum (4, - 72)

Maximum (- 2, 36), Minimum (4, - 72)

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

y = \frac{( x ( z + 2 ) )}{7}

- \frac{x ^{4}}{4} + \frac{x ^{2}}{4}

f (x, y) = - 9 x^{2} - 2 y^{2} + 5 x - 9 y + 10

f (x) = \frac{18}{x ^{2} + 2}

What is the extreme x^3-3x^2-24x+8 ?
The extreme x^3-3x^2-24x+8 is Maximum(-2,36),Minimum(4,-72)