What is the extreme f(x)=-x^4-4x^3+7 ?

The extreme f(x)=-x^4-4x^3+7 is Maximum(-3,34),Saddle(0,7)

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extreme f(x)=-x^4-4x^3+7

extreme points

f (x) = - x^{4} - 4 x^{3} + 7

Maximum (- 3, 34), Saddle (0, 7)

Solution steps

f^{'} (x) = - 4 x^{3} - 12 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 3

into

- x^{4} - 4 x^{3} + 7 : 34

Maximum (- 3, 34)

Plug

x = 0

into

- x^{4} - 4 x^{3} + 7 : 7

Saddle (0, 7)

Maximum (- 3, 34), Saddle (0, 7)

What is the extreme f(x)=-x^4-4x^3+7 ?
The extreme f(x)=-x^4-4x^3+7 is Maximum(-3,34),Saddle(0,7)