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Popular >

extreme f(x)=6x+6/x

Solution

extreme points

f (x) = 6 x + \frac{6}{x}

Solution

Maximum (- 1, - 12), Minimum (1, 12)

Solution steps

f^{'} (x) = 6 - \frac{6}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

6 x + \frac{6}{x} : - 12

Maximum (- 1, - 12)

Plug

x = 1

into

6 x + \frac{6}{x} : 12

Minimum (1, 12)

Maximum (- 1, - 12), Minimum (1, 12)

Popular Examples

extreme f(x,y)=x^2-3xy-y^2 extreme points

f (x, y) = x^{2} - 3 x y - y^{2}

extreme p(x)=12x^4-27x^3+ax^2+27x-6 extreme points

p (x) = 12 x^{4} - 27 x^{3} + a x^{2} + 27 x - 6

extreme f(x,y)=x^3-3x+y^2+6y+8 extreme points

f (x, y) = x^{3} - 3 x + y^{2} + 6 y + 8

extreme f(x,y)=8+76xy+38x^2+240y+(y^4)/4 extreme points

f (x, y) = 8 + 76 x y + 38 x^{2} + 240 y + \frac{y ^{4}}{4}

extreme y=(x^2)/(ln(x))extreme points

y = \frac{x ^{2}}{ln ( x )}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=6x+6/x ?
The extreme f(x)=6x+6/x is Maximum(-1,-12),Minimum(1,12)