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Popular >

extreme f(x)=4x^3-8x

Solution

extreme points

f (x) = 4 x^{3} - 8 x

Solution

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}), Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Solution steps

f^{'} (x) = 12 x^{2} - 8

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

4 x^{3} - 8 x : - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3})

Plug

x = \frac{2}{3}

into

4 x^{3} - 8 x : 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3}

Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}), Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Popular Examples

extreme f(x)=12x^5+45x^4-360x^3+6 extreme points

f (x) = 12 x^{5} + 45 x^{4} - 360 x^{3} + 6

extreme f(x)=(x^2+3x-1)^{1/3}extreme points

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

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

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

extreme f(x,y)=(20000)/(3+x^2+y^2)extreme points

f (x, y) = \frac{20000}{3 + x ^{2} + y ^{2}}

extreme f(x)=2x^3-15x^2+24x,0<= x<= 5 extreme points

f (x) = 2 x^{3} - 15 x^{2} + 24 x, 0 \leq x \leq 5

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^3-8x ?
The extreme f(x)=4x^3-8x is