What is the extreme f(x)=240x+57x^2-x^3 ?

The extreme f(x)=240x+57x^2-x^3 is Minimum(-2,-244),Maximum(40,36800)

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extreme f(x)=240x+57x^2-x^3

extreme points

f (x) = 240 x + 57 x^{2} - x^{3}

Minimum (- 2, - 244), Maximum (40, 36800)

Solution steps

f^{'} (x) = 240 + 114 x - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 40,

Decreasing

: 40 < x < \infty

Plug

x = - 2

into

240 x + 57 x^{2} - x^{3} : - 244

Minimum (- 2, - 244)

Plug

x = 40

into

240 x + 57 x^{2} - x^{3} : 36800

Maximum (40, 36800)

Minimum (- 2, - 244), Maximum (40, 36800)

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

f (x) = x^{2} + 2 x + 5

\frac{x ^{2} - 12}{x - 4}

f (x) = - 4 x + 5 ln (2 x)

f (x, y) = x^{3} + 4 y^{2} - 3 x + 1

What is the extreme f(x)=240x+57x^2-x^3 ?
The extreme f(x)=240x+57x^2-x^3 is Minimum(-2,-244),Maximum(40,36800)