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Popular >

extreme x^3+x^2-5x+1

Solution

extreme points

x^{3} + x^{2} - 5 x + 1

Solution

Maximum (- \frac{5}{3}, \frac{202}{27}), Minimum (1, - 2)

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 + 1 : \frac{202}{27}

Maximum (- \frac{5}{3}, \frac{202}{27})

Plug

x = 1

into

x^{3} + x^{2} - 5 x + 1 : - 2

Minimum (1, - 2)

Maximum (- \frac{5}{3}, \frac{202}{27}), Minimum (1, - 2)

Popular Examples

extreme f(x)=3.6x^5+4x^3-3.7x,0<= x<= 1 extreme points

f (x) = 3.6 x^{5} + 4 x^{3} - 3.7 x, 0 \leq x \leq 1

extreme ln(x^2+4)extreme points

ln (x^{2} + 4)

extreme f(x)=x^4-32x^2+10 extreme points

f (x) = x^{4} - 32 x^{2} + 10

extreme f(x)=x^3+y^3+3x^2-9y^2-1 extreme points

f (x) = x^{3} + y^{3} + 3 x^{2} - 9 y^{2} - 1

extreme (x^2)/(x^2+243)extreme points

\frac{x ^{2}}{x ^{2} + 243}

Frequently Asked Questions (FAQ)

What is the extreme x^3+x^2-5x+1 ?
The extreme x^3+x^2-5x+1 is Maximum(-5/3 , 202/27),Minimum(1,-2)