What is the extreme x(57-x^2) ?

The extreme x(57-x^2) is Minimum(-sqrt(19),-38sqrt(19)),Maximum(sqrt(19),38sqrt(19))

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extreme x(57-x^2)

extreme points

x (57 - x^{2})

Minimum (- 19, - 3819), Maximum (19, 3819)

Solution steps

f^{'} (x) = - 3 (x + 19) (x - 19)

Find intervals:

Decreasing

: - \infty < x < - 19,

Increasing

: - 19 < x < 19,

Decreasing

: 19 < x < \infty

Plug

x = - 19

into

x (57 - x^{2}) : - 3819

Minimum (- 19, - 3819)

Plug

x = 19

into

x (57 - x^{2}) : 3819

Maximum (19, 3819)

Minimum (- 19, - 3819), Maximum (19, 3819)

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 7

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 6

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 1

Q (a, b) = 7 a (a - 2 b) + a (a - 3 b) + 2 a^{2} - 8 b^{2}

g (y, z) = y^{2} z^{3} + π yz

What is the extreme x(57-x^2) ?
The extreme x(57-x^2) is Minimum(-sqrt(19),-38sqrt(19)),Maximum(sqrt(19),38sqrt(19))