What is the extreme f(x)=-2x^3+24x^2+54x+41 ?

The extreme f(x)=-2x^3+24x^2+54x+41 is Minimum(-1,13),Maximum(9,1013)

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extreme f(x)=-2x^3+24x^2+54x+41

extreme points

f (x) = - 2 x^{3} + 24 x^{2} + 54 x + 41

Minimum (- 1, 13), Maximum (9, 1013)

Solution steps

f^{'} (x) = - 6 x^{2} + 48 x + 54

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 9,

Decreasing

: 9 < x < \infty

Plug

x = - 1

into

- 2 x^{3} + 24 x^{2} + 54 x + 41 : 13

Minimum (- 1, 13)

Plug

x = 9

into

- 2 x^{3} + 24 x^{2} + 54 x + 41 : 1013

Maximum (9, 1013)

Minimum (- 1, 13), Maximum (9, 1013)

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

f (x) = x^{3} + 3 x^{2} + 3 x + 1

16 (x - 1)^{4} - 4 (x - 1)^{2} + 1

f (x, y) = x^{2} + 3 x y + y - 1

f (x y) = x^{3} + y^{3} + 3 x^{2} - 18 y + 5

What is the extreme f(x)=-2x^3+24x^2+54x+41 ?
The extreme f(x)=-2x^3+24x^2+54x+41 is Minimum(-1,13),Maximum(9,1013)