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Popular >

extreme (x^3+1)/x

Solution

extreme points

\frac{x ^{3} + 1}{x}

Solution

Minimum (\frac{1}{3 2}, \frac{3}{2 ^{\frac{2}{3}}})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{3 2},

Increasing

: \frac{1}{3 2} < x < \infty

Plug

x = \frac{1}{3 2}

into

\frac{x ^{3} + 1}{x} : \frac{3}{2 ^{\frac{2}{3}}}

Minimum (\frac{1}{3 2}, \frac{3}{2 ^{\frac{2}{3}}})

Graph

Popular Examples

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

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

extreme y=ln(x^2)+8x+24 extreme points

y = ln (x^{2}) + 8 x + 24

extreme f(x)=x^3-2x^2-4x+8,-1<= x<= 0 extreme points

f (x) = x^{3} - 2 x^{2} - 4 x + 8, - 1 \leq x \leq 0

extreme f(x)= 1/(3x^3+2x^2+3x)extreme points

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

extreme T(x,y)=(|x|,2y)extreme points

T (x, y) = (∣ x ∣, 2 y)

Frequently Asked Questions (FAQ)

What is the extreme (x^3+1)/x ?
The extreme (x^3+1)/x is Minimum(1/(\sqrt[3]{2)}, 3/(2^{2/3)})