What is the extreme f(x)=x^3-12x^2+80 ?

The extreme f(x)=x^3-12x^2+80 is Maximum(0,80),Minimum(8,-176)

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extreme f(x)=x^3-12x^2+80

extreme points

f (x) = x^{3} - 12 x^{2} + 80

Maximum (0, 80), Minimum (8, - 176)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 0

into

x^{3} - 12 x^{2} + 80 : 80

Maximum (0, 80)

Plug

x = 8

into

x^{3} - 12 x^{2} + 80 : - 176

Minimum (8, - 176)

Maximum (0, 80), Minimum (8, - 176)

f (x) = 20 y - 2 x^{2} - 4 x y - y^{2} + 30 x

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

f (x, y) = x^{2} y + 12 x^{2} + \frac{3 y ^{2}}{2} + 5

f (x) = x^{\frac{2}{3}}, - 1 \leq x \leq 27

f (x) = \frac{1}{4} x^{4} - 2 x^{3} + 4

What is the extreme f(x)=x^3-12x^2+80 ?
The extreme f(x)=x^3-12x^2+80 is Maximum(0,80),Minimum(8,-176)