What is the extreme y=5+12x^2-8x^3 ?

The extreme y=5+12x^2-8x^3 is Minimum(0,5),Maximum(1,9)

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extreme y=5+12x^2-8x^3

extreme points

y = 5 + 12 x^{2} - 8 x^{3}

Minimum (0, 5), Maximum (1, 9)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

5 + 12 x^{2} - 8 x^{3} : 5

Minimum (0, 5)

Plug

x = 1

into

5 + 12 x^{2} - 8 x^{3} : 9

Maximum (1, 9)

Minimum (0, 5), Maximum (1, 9)

(x + 2) (x + 1) (x - 1) (x - 3)

f (x) = \cdot 0.002 d^{2} + 0.7 d + 6.9

f (x) = x + 16 y^{2} - x^{2} + x y - 3 y^{2} + 25

f (x, y) = 3 x^{2} + 3 y^{2} - 6 x + 12 y

\frac{3 x}{x ^{2} - 1}

What is the extreme y=5+12x^2-8x^3 ?
The extreme y=5+12x^2-8x^3 is Minimum(0,5),Maximum(1,9)