What is the extreme y=2x^3-12x^2+9 ?

The extreme y=2x^3-12x^2+9 is Maximum(0,9),Minimum(4,-55)

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extreme y=2x^3-12x^2+9

extreme points

y = 2 x^{3} - 12 x^{2} + 9

Maximum (0, 9), Minimum (4, - 55)

Solution steps

f^{'} (x) = 6 x^{2} - 24 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

2 x^{3} - 12 x^{2} + 9 : 9

Maximum (0, 9)

Plug

x = 4

into

2 x^{3} - 12 x^{2} + 9 : - 55

Minimum (4, - 55)

Maximum (0, 9), Minimum (4, - 55)

\frac{8}{x} + 2 π x^{2}

f (x, y) = 8 x \frac{5}{6} y \frac{1}{6}

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

f (x) = e^{x - [x]}

f (x, y) = x^{2} + x y + y^{2} + 5 x - 2 y + 1

What is the extreme y=2x^3-12x^2+9 ?
The extreme y=2x^3-12x^2+9 is Maximum(0,9),Minimum(4,-55)