What is the extreme f(x)=-2x^3+18x^2-48x+19 ?

The extreme f(x)=-2x^3+18x^2-48x+19 is Minimum(2,-21),Maximum(4,-13)

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extreme f(x)=-2x^3+18x^2-48x+19

extreme points

f (x) = - 2 x^{3} + 18 x^{2} - 48 x + 19

Minimum (2, - 21), Maximum (4, - 13)

Solution steps

f^{'} (x) = - 6 x^{2} + 36 x - 48

Find intervals:

Decreasing

: - \infty < x < 2,

Increasing

: 2 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 2

into

- 2 x^{3} + 18 x^{2} - 48 x + 19 : - 21

Minimum (2, - 21)

Plug

x = 4

into

- 2 x^{3} + 18 x^{2} - 48 x + 19 : - 13

Maximum (4, - 13)

Minimum (2, - 21), Maximum (4, - 13)

f (x) = x^{2} - 1

f (x) = sin (4 x)

f (x) = x + 2 y

f (x) = - x^{3} + 3 x - 7

f (x, y) = x^{2} + 4 y^{2} - 6 x + 16 y

What is the extreme f(x)=-2x^3+18x^2-48x+19 ?
The extreme f(x)=-2x^3+18x^2-48x+19 is Minimum(2,-21),Maximum(4,-13)