What is the extreme f(x)=2(3x+2)^2-3x^4 ?

The extreme f(x)=2(3x+2)^2-3x^4 is Saddle(-1,-1),Maximum(2,80)

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extreme f(x)=2(3x+2)^2-3x^4

extreme points

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

Saddle (- 1, - 1), Maximum (2, 80)

Solution steps

f^{'} (x) = - 12 (x + 1)^{2} (x - 2)

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 1

into

2 (3 x + 2)^{2} - 3 x^{4} : - 1

Saddle (- 1, - 1)

Plug

x = 2

into

2 (3 x + 2)^{2} - 3 x^{4} : 80

Maximum (2, 80)

Saddle (- 1, - 1), Maximum (2, 80)

y = x (x + 4)^{3}

f (x) = \frac{4 x}{x ^{2} - 49}

f (x) = x^{3} - 6 x^{2} + 8, - 1 \leq x \leq 6

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

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

What is the extreme f(x)=2(3x+2)^2-3x^4 ?
The extreme f(x)=2(3x+2)^2-3x^4 is Saddle(-1,-1),Maximum(2,80)