What is the extreme f(x)=12x^5+30x^4-300x^3+3 ?

The extreme f(x)=12x^5+30x^4-300x^3+3 is Maximum(-5,18753),Saddle(0,3),Minimum(3,-2751)

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extreme f(x)=12x^5+30x^4-300x^3+3

extreme points

f (x) = 12 x^{5} + 30 x^{4} - 300 x^{3} + 3

Maximum (- 5, 18753), Saddle (0, 3), Minimum (3, - 2751)

Solution steps

f^{'} (x) = 60 x^{4} + 120 x^{3} - 900 x^{2}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 5

into

12 x^{5} + 30 x^{4} - 300 x^{3} + 3 : 18753

Maximum (- 5, 18753)

Plug

x = 0

into

12 x^{5} + 30 x^{4} - 300 x^{3} + 3 : 3

Saddle (0, 3)

Plug

x = 3

into

12 x^{5} + 30 x^{4} - 300 x^{3} + 3 : - 2751

Minimum (3, - 2751)

Maximum (- 5, 18753), Saddle (0, 3), Minimum (3, - 2751)

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g (y) = 4 - y^{2}, - 2 \leq y \leq 1

f (x) = \frac{( x ^{2} - 8 )}{x + 3}

What is the extreme f(x)=12x^5+30x^4-300x^3+3 ?
The extreme f(x)=12x^5+30x^4-300x^3+3 is Maximum(-5,18753),Saddle(0,3),Minimum(3,-2751)