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Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{1}{6}, - \frac{2}{3 3} + \frac{2}{3} + 3), Minimum (\frac{1}{6}, \frac{2}{3 3} - \frac{2}{3} + 3)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{1}{6},

Decreasing

: - \frac{1}{6} < x < \frac{1}{6},

Increasing

: \frac{1}{6} < x < \infty

Plug

x = - \frac{1}{6}

into

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

Maximum (- \frac{1}{6}, - \frac{2}{3 3} + \frac{2}{3} + 3)

Plug

x = \frac{1}{6}

into

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

Minimum (\frac{1}{6}, \frac{2}{3 3} - \frac{2}{3} + 3)

Maximum (- \frac{1}{6}, - \frac{2}{3 3} + \frac{2}{3} + 3), Minimum (\frac{1}{6}, \frac{2}{3 3} - \frac{2}{3} + 3)

Popular Examples

extreme f(x,y)=x^2+xy+y^2-16y+85 extreme points

f (x, y) = x^{2} + x y + y^{2} - 16 y + 85

extreme f(x)=4-5x+x^2 extreme points

f (x) = 4 - 5 x + x^{2}

extreme f(x,y)=x^2+xy+y^2-19y+120 extreme points

f (x, y) = x^{2} + x y + y^{2} - 19 y + 120

extreme f(x)=5-4x-x^3 extreme points

f (x) = 5 - 4 x - x^{3}

extreme f(x)=x^3+6x^2-5,-5<= x<= 2 extreme points

f (x) = x^{3} + 6 x^{2} - 5, - 5 \leq x \leq 2

Frequently Asked Questions (FAQ)

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