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Popular >

extreme y=x^4-2x^3

Solution

extreme points

y = x^{4} - 2 x^{3}

Solution

Saddle (0, 0), Minimum (\frac{3}{2}, - \frac{27}{16})

Solution steps

f^{'} (x) = 4 x^{3} - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < \infty

Plug

x = 0

into

x^{4} - 2 x^{3} : 0

Saddle (0, 0)

Plug

x = \frac{3}{2}

into

x^{4} - 2 x^{3} : - \frac{27}{16}

Minimum (\frac{3}{2}, - \frac{27}{16})

Saddle (0, 0), Minimum (\frac{3}{2}, - \frac{27}{16})

Popular Examples

extreme f(x)=((x^2+x+4))/(3+x^2)extreme points

f (x) = \frac{( x ^{2} + x + 4 )}{3 + x ^{2}}

extreme f(x)=x^3-6x+9x-2 extreme points

f (x) = x^{3} - 6 x + 9 x - 2

extreme f(x)=x^3-12x,0<= x<= 5 extreme points

f (x) = x^{3} - 12 x, 0 \leq x \leq 5

extreme f(x)=2x^3-6x^2+4 extreme points

f (x) = 2 x^{3} - 6 x^{2} + 4

extreme f(x)=3x-9x^{1/3}extreme points

f (x) = 3 x - 9 x^{\frac{1}{3}}

Frequently Asked Questions (FAQ)

What is the extreme y=x^4-2x^3 ?
The extreme y=x^4-2x^3 is Saddle(0,0),Minimum(3/2 ,-27/16)