What is the extreme 2x^5-15x^4+30x^3-6 ?

The extreme 2x^5-15x^4+30x^3-6 is Saddle(0,-6),Saddle(3,75)

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extreme 2x^5-15x^4+30x^3-6

extreme points

2 x^{5} - 15 x^{4} + 30 x^{3} - 6

Saddle (0, - 6), Saddle (3, 75)

Solution steps

Find the critical points:

x = 0, x = 3

Domain of

2 x^{5} - 15 x^{4} + 30 x^{3} - 6 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug the extreme point

x = 0

into

2 x^{5} - 15 x^{4} + 30 x^{3} - 6 \Rightarrow y = - 6

Saddle (0, - 6)

Plug the extreme point

x = 3

into

2 x^{5} - 15 x^{4} + 30 x^{3} - 6 \Rightarrow y = 75

Saddle (3, 75)

Saddle (0, - 6), Saddle (3, 75)

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

p (a, c) = a + 8 + c

f (x) = - 2 - x - x^{2}

f (x) = \frac{x - 1}{x ^{2} + 3 x}

e^{3 x^{2} - x - 3}

What is the extreme 2x^5-15x^4+30x^3-6 ?
The extreme 2x^5-15x^4+30x^3-6 is Saddle(0,-6),Saddle(3,75)