What is the extreme f(x)=-x^4+4x^3+9x-6 ?

The extreme f(x)=-x^4+4x^3+9x-6 is Maximum(3.21736…,49.02143…)

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extreme f(x)=-x^4+4x^3+9x-6

extreme points

f (x) = - x^{4} + 4 x^{3} + 9 x - 6

Maximum (3.21736 \dots, 49.02143 \dots)

Solution steps

Find the critical points:

x \approx 3.21736 \dots

Domain of

- x^{4} + 4 x^{3} + 9 x - 6 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 3.21736 \dots,

Decreasing

: 3.21736 \dots < x < \infty

Plug the extreme point

x = 3.21736 \dots

into

- x^{4} + 4 x^{3} + 9 x - 6 \Rightarrow y = 49.02143 \dots

Maximum (3.21736 \dots, 49.02143 \dots)

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

f (x, y) = - 3 x^{2} - 6 y^{2} - 6 x y + 66 x + 102 y

89 e^{x^{4}}

- 4.9 x^{2} + 10 x + 3

f (x) = e^{x} \frac{1}{x ^{5}}, (0, \infty)

What is the extreme f(x)=-x^4+4x^3+9x-6 ?
The extreme f(x)=-x^4+4x^3+9x-6 is Maximum(3.21736…,49.02143…)