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Popular >

extreme f(x)=8x+2/x

Solution

extreme points

f (x) = 8 x + \frac{2}{x}

Solution

Maximum (- \frac{1}{2}, - 8), Minimum (\frac{1}{2}, 8)

Solution steps

f^{'} (x) = 8 - \frac{2}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{1}{2}

into

8 x + \frac{2}{x} : - 8

Maximum (- \frac{1}{2}, - 8)

Plug

x = \frac{1}{2}

into

8 x + \frac{2}{x} : 8

Minimum (\frac{1}{2}, 8)

Maximum (- \frac{1}{2}, - 8), Minimum (\frac{1}{2}, 8)

Popular Examples

extreme s^2-4s+5 extreme points

s^{2} - 4 s + 5

extreme-0.05x^2+20x+1000 extreme points

- 0.05 x^{2} + 20 x + 1000

extreme f(x)=x^3-3/2 x^2,-3<= x<= 4 extreme points

f (x) = x^{3} - \frac{3}{2} x^{2}, - 3 \leq x \leq 4

extreme f(x)= 2/(x+4)extreme points

f (x) = \frac{2}{x + 4}

extreme f(x)=sqrt(2x^2-4x+7)extreme points

f (x) = 2 x^{2} - 4 x + 7

Frequently Asked Questions (FAQ)

What is the extreme f(x)=8x+2/x ?
The extreme f(x)=8x+2/x is Maximum(-1/2 ,-8),Minimum(1/2 ,8)