What is the extreme f(x)=36+3x^2-2x^3 ?

The extreme f(x)=36+3x^2-2x^3 is Minimum(0,36),Maximum(1,37)

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extreme f(x)=36+3x^2-2x^3

extreme points

f (x) = 36 + 3 x^{2} - 2 x^{3}

Minimum (0, 36), Maximum (1, 37)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

36 + 3 x^{2} - 2 x^{3} : 36

Minimum (0, 36)

Plug

x = 1

into

36 + 3 x^{2} - 2 x^{3} : 37

Maximum (1, 37)

Minimum (0, 36), Maximum (1, 37)

f (x) = 3 x^{5} + 5 x^{3}

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

f (x) = 4 x + 9 x^{- 1}

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

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

What is the extreme f(x)=36+3x^2-2x^3 ?
The extreme f(x)=36+3x^2-2x^3 is Minimum(0,36),Maximum(1,37)