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Popular >

extreme f(x)=2x^3-4x-1

Solution

extreme points

f (x) = 2 x^{3} - 4 x - 1

Solution

Maximum (- \frac{2}{3}, - 2 (\frac{2}{3})^{\frac{3}{2}} + 4 \frac{2}{3} - 1), Minimum (\frac{2}{3}, 2 (\frac{2}{3})^{\frac{3}{2}} - 4 \frac{2}{3} - 1)

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

Maximum (- \frac{2}{3}, - 2 (\frac{2}{3})^{\frac{3}{2}} + 4 \frac{2}{3} - 1)

Plug

x = \frac{2}{3}

into

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

Minimum (\frac{2}{3}, 2 (\frac{2}{3})^{\frac{3}{2}} - 4 \frac{2}{3} - 1)

Maximum (- \frac{2}{3}, - 2 (\frac{2}{3})^{\frac{3}{2}} + 4 \frac{2}{3} - 1), Minimum (\frac{2}{3}, 2 (\frac{2}{3})^{\frac{3}{2}} - 4 \frac{2}{3} - 1)

Popular Examples

extreme y=0.25t^4-4.5t^2 extreme points

y = 0.25 t^{4} - 4.5 t^{2}

extreme y=10x-11z extreme points

y = 10 x - 11 z

extreme f(x)=3x^2+12x+7/8 extreme points

f (x) = 3 x^{2} + 12 x + \frac{7}{8}

extreme f(x)=(x^3-64)^4 extreme points

f (x) = (x^{3} - 64)^{4}

extreme f(x,y)=7x^2+7xy+10y^2+7xy^2+4x^2y extreme points

f (x, y) = 7 x^{2} + 7 x y + 10 y^{2} + 7 x y^{2} + 4 x^{2} y

Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x^3-4x-1 ?
The extreme f(x)=2x^3-4x-1 is