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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

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

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

Popular Examples

domain of g(t)=-3/(2t^{3/2)}domain

g (t) = - \frac{3}{2 t ^{\frac{3}{2}}}

range of 5+(6+x)^{1/2}range

5 + (6 + x)^{\frac{1}{2}}

domain of (x^2-4)/(x-2)domain

\frac{x ^{2} - 4}{x - 2}

intercepts of y=2x intercepts

y = 2 x

inverse of sqrt(x^2+7x)inverse

x^{2} + 7 x

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2)/2+1/x ?
The extreme f(x)=(x^2)/2+1/x is Minimum(1, 3/2)