What is the extreme f(x)=-2x^3-9x^2+24x+40 ?

The extreme f(x)=-2x^3-9x^2+24x+40 is Minimum(-4,-72),Maximum(1,53)

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extreme f(x)=-2x^3-9x^2+24x+40

extreme points

f (x) = - 2 x^{3} - 9 x^{2} + 24 x + 40

Minimum (- 4, - 72), Maximum (1, 53)

Solution steps

f^{'} (x) = - 6 x^{2} - 18 x + 24

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 4

into

- 2 x^{3} - 9 x^{2} + 24 x + 40 : - 72

Minimum (- 4, - 72)

Plug

x = 1

into

- 2 x^{3} - 9 x^{2} + 24 x + 40 : 53

Maximum (1, 53)

Minimum (- 4, - 72), Maximum (1, 53)

f (x, y) = x^{2} y + y^{3} - 48 y

f (x, y) = (5 x + 3 y + 10) (4 y + 2)

f (x) = x^{3} - 9 x

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

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

What is the extreme f(x)=-2x^3-9x^2+24x+40 ?
The extreme f(x)=-2x^3-9x^2+24x+40 is Minimum(-4,-72),Maximum(1,53)