What is the extreme f(x)=-x^3+27x-61 ?

The extreme f(x)=-x^3+27x-61 is Minimum(-3,-115),Maximum(3,-7)

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extreme f(x)=-x^3+27x-61

extreme points

f (x) = - x^{3} + 27 x - 61

Minimum (- 3, - 115), Maximum (3, - 7)

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 - 61 : - 115

Minimum (- 3, - 115)

Plug

x = 3

into

- x^{3} + 27 x - 61 : - 7

Maximum (3, - 7)

Minimum (- 3, - 115), Maximum (3, - 7)

f (x) = 2 sec (x), - \frac{π}{3} \leq x \leq \frac{π}{3}

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

- x^{3} - 6 x^{2}

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

f (x) = \frac{x ^{3}}{4 - x ^{2}}

What is the extreme f(x)=-x^3+27x-61 ?
The extreme f(x)=-x^3+27x-61 is Minimum(-3,-115),Maximum(3,-7)