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

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

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extreme x^4-x^3-3x^2+5x-2

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

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

Increasing

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

Increasing

: 1 < x < \infty

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})

Plug

x = 1

into

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

Saddle (1, 0)

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

2 x^{3} + 9 x y^{2} + 15 x^{2} + 27 y^{2}

f (x, y) = e^{x^{2} + y^{2} - 4 y}

g (x, y) = x y^{2} + x^{2} + y

K (r, s) = 6 r - s

f (x) = 7 x^{5} + 3 x^{3} - 2 x^{2} + x - 8

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