What is the extreme f(x)=-x^3+27x-51 ?

The extreme f(x)=-x^3+27x-51 is Minimum(-3,-105),Maximum(3,3)

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extreme f(x)=-x^3+27x-51

extreme points

f (x) = - x^{3} + 27 x - 51

Minimum (- 3, - 105), Maximum (3, 3)

Solution steps

f^{'} (x) = - 3 x^{2} + 27

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

- x^{3} + 27 x - 51 : - 105

Minimum (- 3, - 105)

Plug

x = 3

into

- x^{3} + 27 x - 51 : 3

Maximum (3, 3)

Minimum (- 3, - 105), Maximum (3, 3)

f (x) = - x^{3} + 27 x - 63

f (x) = 3 x^{2} - 9 y^{2}

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

f (x) = - x^{3} + 12 x^{2}

f (x) = 3 x + 2 y

What is the extreme f(x)=-x^3+27x-51 ?
The extreme f(x)=-x^3+27x-51 is Minimum(-3,-105),Maximum(3,3)