What is the extreme f(x)=x^4+x^3-3x^2-5x-2 ?

The extreme f(x)=x^4+x^3-3x^2-5x-2 is Saddle(-1,0),Minimum(5/4 ,-2187/256)

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extreme f(x)=x^4+x^3-3x^2-5x-2

extreme points

f (x) = x^{4} + x^{3} - 3 x^{2} - 5 x - 2

Saddle (- 1, 0), Minimum (\frac{5}{4}, - \frac{2187}{256})

Solution steps

f^{'} (x) = 4 x^{3} + 3 x^{2} - 6 x - 5

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{5}{4},

Increasing

: \frac{5}{4} < x < \infty

Plug

x = - 1

into

x^{4} + x^{3} - 3 x^{2} - 5 x - 2 : 0

Saddle (- 1, 0)

Plug

x = \frac{5}{4}

into

x^{4} + x^{3} - 3 x^{2} - 5 x - 2 : - \frac{2187}{256}

Minimum (\frac{5}{4}, - \frac{2187}{256})

Saddle (- 1, 0), Minimum (\frac{5}{4}, - \frac{2187}{256})

f (x) = cos (π x), 0 \leq x \leq \frac{1}{6}

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

f (x, y) = 6 e^{- 2 x - 2 y}

f (x) = 45 - 3 x

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

What is the extreme f(x)=x^4+x^3-3x^2-5x-2 ?
The extreme f(x)=x^4+x^3-3x^2-5x-2 is Saddle(-1,0),Minimum(5/4 ,-2187/256)