What is the extreme f(x)=2x^3-36x^2+120x+2 ?

The extreme f(x)=2x^3-36x^2+120x+2 is Maximum(2,114),Minimum(10,-398)

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extreme f(x)=2x^3-36x^2+120x+2

extreme points

f (x) = 2 x^{3} - 36 x^{2} + 120 x + 2

Maximum (2, 114), Minimum (10, - 398)

Solution steps

f^{'} (x) = 6 x^{2} - 72 x + 120

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 10,

Increasing

: 10 < x < \infty

Plug

x = 2

into

2 x^{3} - 36 x^{2} + 120 x + 2 : 114

Maximum (2, 114)

Plug

x = 10

into

2 x^{3} - 36 x^{2} + 120 x + 2 : - 398

Minimum (10, - 398)

Maximum (2, 114), Minimum (10, - 398)

4 sin^{2} (x)

2 y^{3} - 12 y x + 3 x^{2} + 18 y

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

\frac{5 - x}{x + 2}

f (x) = x^{2} - 9 x + 14

What is the extreme f(x)=2x^3-36x^2+120x+2 ?
The extreme f(x)=2x^3-36x^2+120x+2 is Maximum(2,114),Minimum(10,-398)