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Popular >

extreme x+(64)/x

Solution

extreme points

x + \frac{64}{x}

Solution

Maximum (- 8, - 16), Minimum (8, 16)

Solution steps

f^{'} (x) = 1 - \frac{64}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 8,

Decreasing

: - 8 < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = - 8

into

x + \frac{64}{x} : - 16

Maximum (- 8, - 16)

Plug

x = 8

into

x + \frac{64}{x} : 16

Minimum (8, 16)

Maximum (- 8, - 16), Minimum (8, 16)

Popular Examples

extreme f(x)=x^3-6x^2-15x+10 extreme points

f (x) = x^{3} - 6 x^{2} - 15 x + 10

extreme f(x)=x^4-32x^2+6 extreme points

f (x) = x^{4} - 32 x^{2} + 6

extreme f(x)= x/((x-1)^2)extreme points

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

extreme f(x,y)=2^2x^4+2^2y^4-4xy+16 extreme points

f (x, y) = 2^{2} x^{4} + 2^{2} y^{4} - 4 x y + 16

extreme f(x)=Ix-3I-2 extreme points

f (x) = I x - 3 I - 2

Frequently Asked Questions (FAQ)

What is the extreme x+(64)/x ?
The extreme x+(64)/x is Maximum(-8,-16),Minimum(8,16)