What is the extreme f(x)=2x^3-6x^2+30 ?

The extreme f(x)=2x^3-6x^2+30 is Maximum(0,30),Minimum(2,22)

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extreme f(x)=2x^3-6x^2+30

extreme points

f (x) = 2 x^{3} - 6 x^{2} + 30

Maximum (0, 30), Minimum (2, 22)

Solution steps

f^{'} (x) = 6 x^{2} - 12 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

2 x^{3} - 6 x^{2} + 30 : 30

Maximum (0, 30)

Plug

x = 2

into

2 x^{3} - 6 x^{2} + 30 : 22

Minimum (2, 22)

Maximum (0, 30), Minimum (2, 22)

\frac{1}{9} x^{4} - \frac{4}{9} x^{3}

g (x) = \frac{1}{x} - 1

y = - 3 x - 9

f (x) = x^{3} - 1

f (x) = \frac{x ^{3} + 2 x + 1}{x ^{2} - 5 x}

What is the extreme f(x)=2x^3-6x^2+30 ?
The extreme f(x)=2x^3-6x^2+30 is Maximum(0,30),Minimum(2,22)