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

The extreme f(x)=P(x)=x^3+x^2-5x+3 is Maximum(-5/3 , 256/27),Minimum(1,0)

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

extreme points

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

Maximum (- \frac{5}{3}, \frac{256}{27}), Minimum (1, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{5}{3}

into

x^{3} + x^{2} - 5 x + 3 : \frac{256}{27}

Maximum (- \frac{5}{3}, \frac{256}{27})

Plug

x = 1

into

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

Minimum (1, 0)

Maximum (- \frac{5}{3}, \frac{256}{27}), Minimum (1, 0)

2 x^{3} - 3 x^{2} - 12 x + 12

f (x) = \frac{10 x}{1 + x ^{2}}

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

f (x) = x^{3} - 3 x + 1, 0 \leq x \leq 5

What is the extreme f(x)=P(x)=x^3+x^2-5x+3 ?
The extreme f(x)=P(x)=x^3+x^2-5x+3 is Maximum(-5/3 , 256/27),Minimum(1,0)