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Popular >

extreme 1/4 x^4-2x^3+3x^2+2

Solution

extreme points

\frac{1}{4} x^{4} - 2 x^{3} + 3 x^{2} + 2

Solution

Minimum (0, 2), Maximum (3 - 3, \frac{( 3 - 3 ) ^{4}}{4} + 423 - 70), Minimum (3 + 3, \frac{( 3 + 3 ) ^{4}}{4} - 70 - 423)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 3 - 3,

Decreasing

: 3 - 3 < x < 3 + 3,

Increasing

: 3 + 3 < x < \infty

Plug

x = 0

into

\frac{1}{4} x^{4} - 2 x^{3} + 3 x^{2} + 2 : 2

Minimum (0, 2)

Plug

x = 3 - 3

into

\frac{1}{4} x^{4} - 2 x^{3} + 3 x^{2} + 2 : \frac{( 3 - 3 ) ^{4}}{4} + 423 - 70

Maximum (3 - 3, \frac{( 3 - 3 ) ^{4}}{4} + 423 - 70)

Plug

x = 3 + 3

into

\frac{1}{4} x^{4} - 2 x^{3} + 3 x^{2} + 2 : \frac{( 3 + 3 ) ^{4}}{4} - 70 - 423

Minimum (3 + 3, \frac{( 3 + 3 ) ^{4}}{4} - 70 - 423)

Minimum (0, 2), Maximum (3 - 3, \frac{( 3 - 3 ) ^{4}}{4} + 423 - 70), Minimum (3 + 3, \frac{( 3 + 3 ) ^{4}}{4} - 70 - 423)

Popular Examples

extreme f(x)=x+(16)/x ,0.2<= x<= 16 extreme points

f (x) = x + \frac{16}{x}, 0.2 \leq x \leq 16

extreme f(x)=3x^{5/3}-2x^{2/3}extreme points

f (x) = 3 x^{\frac{5}{3}} - 2 x^{\frac{2}{3}}

extreme g(x)=-x^3+3x-10 extreme points

g (x) = - x^{3} + 3 x - 10

extreme f(x)= 1/20 x^2-25sqrt(x)extreme points

f (x) = \frac{1}{20} x^{2} - 25 x

extreme f(x)=3x^3+9/2 x^2-54x+1 extreme points

f (x) = 3 x^{3} + \frac{9}{2} x^{2} - 54 x + 1

Frequently Asked Questions (FAQ)

What is the extreme 1/4 x^4-2x^3+3x^2+2 ?
The extreme 1/4 x^4-2x^3+3x^2+2 is