What is the extreme f(x)=10x^6+24x^5+15x^4+3 ?

The extreme f(x)=10x^6+24x^5+15x^4+3 is Saddle(-1,4),Minimum(0,3)

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extreme f(x)=10x^6+24x^5+15x^4+3

extreme points

f (x) = 10 x^{6} + 24 x^{5} + 15 x^{4} + 3

Saddle (- 1, 4), Minimum (0, 3)

Solution steps

f^{'} (x) = 60 x^{5} + 120 x^{4} + 60 x^{3}

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

10 x^{6} + 24 x^{5} + 15 x^{4} + 3 : 4

Saddle (- 1, 4)

Plug

x = 0

into

10 x^{6} + 24 x^{5} + 15 x^{4} + 3 : 3

Minimum (0, 3)

Saddle (- 1, 4), Minimum (0, 3)

What is the extreme f(x)=10x^6+24x^5+15x^4+3 ?
The extreme f(x)=10x^6+24x^5+15x^4+3 is Saddle(-1,4),Minimum(0,3)