What is the extreme f(x)=-7+6x-x^3 ?

The extreme f(x)=-7+6x-x^3 is Minimum(-sqrt(2),-7-4sqrt(2)),Maximum(sqrt(2),-7+4sqrt(2))

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extreme f(x)=-7+6x-x^3

extreme points

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

Minimum (- 2, - 7 - 42), Maximum (2, - 7 + 42)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- 7 + 6 x - x^{3} : - 7 - 42

Minimum (- 2, - 7 - 42)

Plug

x = 2

into

- 7 + 6 x - x^{3} : - 7 + 42

Maximum (2, - 7 + 42)

Minimum (- 2, - 7 - 42), Maximum (2, - 7 + 42)

f (x) = \frac{2}{6 - 5 x}

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

- \frac{4}{\frac{5}{x} - 5}

x^{3} - 6 x^{2} + 9 x + 1

f (x) = 25 x - x^{2}

What is the extreme f(x)=-7+6x-x^3 ?
The extreme f(x)=-7+6x-x^3 is Minimum(-sqrt(2),-7-4sqrt(2)),Maximum(sqrt(2),-7+4sqrt(2))