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Popular >

extreme x^6-6/5 x^5

Solution

extreme points

x^{6} - \frac{6}{5} x^{5}

Solution

Saddle (0, 0), Minimum (1, - \frac{1}{5})

Solution steps

f^{'} (x) = 6 x^{5} - 6 x^{4}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

x^{6} - \frac{6}{5} x^{5} : 0

Saddle (0, 0)

Plug

x = 1

into

x^{6} - \frac{6}{5} x^{5} : - \frac{1}{5}

Minimum (1, - \frac{1}{5})

Saddle (0, 0), Minimum (1, - \frac{1}{5})

Popular Examples

extreme P(x,y)=0.3+x^2+0.2y^2+0.1xy-14x-10y+2000 extreme points

P (x, y) = 0.3 + x^{2} + 0.2 y^{2} + 0.1 x y - 14 x - 10 y + 2000

extreme f(x,y)= 1/2 x^2+1/2 y^2-x^2y+5 extreme points

f (x, y) = \frac{1}{2} x^{2} + \frac{1}{2} y^{2} - x^{2} y + 5

extreme y=(x^4}{12}-\frac{x^3)/2+x^2+10 extreme points

y = \frac{x ^{4}}{12} - \frac{x ^{3}}{2} + x^{2} + 10

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

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

extreme sin^8(x)+cos^8(x)extreme points

sin^{8} (x) + cos^{8} (x)

Frequently Asked Questions (FAQ)

What is the extreme x^6-6/5 x^5 ?
The extreme x^6-6/5 x^5 is Saddle(0,0),Minimum(1,-1/5)