What is the extreme f(x)=x^4+2x^3-x+x+1 ?

The extreme f(x)=x^4+2x^3-x+x+1 is Minimum(-3/2 ,-11/16),Saddle(0,1)

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extreme f(x)=x^4+2x^3-x+x+1

extreme points

f (x) = x^{4} + 2 x^{3} - x + x + 1

Minimum (- \frac{3}{2}, - \frac{11}{16}), Saddle (0, 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - \frac{3}{2},

Increasing

: - \frac{3}{2} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

x^{4} + 2 x^{3} - x + x + 1 : - \frac{11}{16}

Minimum (- \frac{3}{2}, - \frac{11}{16})

Plug

x = 0

into

x^{4} + 2 x^{3} - x + x + 1 : 1

Saddle (0, 1)

Minimum (- \frac{3}{2}, - \frac{11}{16}), Saddle (0, 1)

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

52900 + 400 x + x^{2}

f (x) = - x - 4, - 4 \leq x \leq 1

f (x, y) = x^{2} - 9 x y - y^{2}

x θ

What is the extreme f(x)=x^4+2x^3-x+x+1 ?
The extreme f(x)=x^4+2x^3-x+x+1 is Minimum(-3/2 ,-11/16),Saddle(0,1)