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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{2}{3}

into

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

Maximum (- \frac{2}{3}, - 2 (\frac{2}{3})^{\frac{3}{2}} + 4 \frac{2}{3} + 4)

Plug

x = \frac{2}{3}

into

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

Minimum (\frac{2}{3}, 2 (\frac{2}{3})^{\frac{3}{2}} - 4 \frac{2}{3} + 4)

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

Popular Examples

extreme P(x,y)=2x+y extreme points

P (x, y) = 2 x + y

extreme y=(5280)/(pix^2)-4/3 x extreme points

y = \frac{5280}{π x ^{2}} - \frac{4}{3} x

extreme x^3-6x^2-15x+2 extreme points

x^{3} - 6 x^{2} - 15 x + 2

extreme x^3-6x^2-15x+4 extreme points

x^{3} - 6 x^{2} - 15 x + 4

extreme x^3-6x^2-15x+6 extreme points

x^{3} - 6 x^{2} - 15 x + 6

Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x^3-4x+4 ?
The extreme f(x)=2x^3-4x+4 is