What is the extreme y=16x^4+64x^3 ?

The extreme y=16x^4+64x^3 is Minimum(-3,-432),Saddle(0,0)

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extreme y=16x^4+64x^3

extreme points

y = 16 x^{4} + 64 x^{3}

Minimum (- 3, - 432), Saddle (0, 0)

Solution steps

f^{'} (x) = 64 x^{3} + 192 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

16 x^{4} + 64 x^{3} : - 432

Minimum (- 3, - 432)

Plug

x = 0

into

16 x^{4} + 64 x^{3} : 0

Saddle (0, 0)

Minimum (- 3, - 432), Saddle (0, 0)

3 x^{2} - 2 x y + y^{2} - 8 y

f (x) = 32 e^{4 x} x - 28 e^{4 x}

f (x) = 12 x - 9 x^{2} + 2 x^{3}

f (x, y) = 5 x^{2} - 4 x y + 4 y^{2} + 12 x + 25

f (x) = 2 x^{3} - \frac{12 x ^{2}}{2} - 2 [- 1.3]

What is the extreme y=16x^4+64x^3 ?
The extreme y=16x^4+64x^3 is Minimum(-3,-432),Saddle(0,0)