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Popular >

extreme f(x)=x^3-7x-6

Solution

extreme points

f (x) = x^{3} - 7 x - 6

Solution

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6), Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6)

Solution steps

f^{'} (x) = 3 x^{2} - 7

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3},

Decreasing

: - \frac{7}{3} < x < \frac{7}{3},

Increasing

: \frac{7}{3} < x < \infty

Plug

x = - \frac{7}{3}

into

x^{3} - 7 x - 6 : - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6)

Plug

x = \frac{7}{3}

into

x^{3} - 7 x - 6 : (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6

Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6)

Maximum (- \frac{7}{3}, - (\frac{7}{3})^{\frac{3}{2}} + 7 \frac{7}{3} - 6), Minimum (\frac{7}{3}, (\frac{7}{3})^{\frac{3}{2}} - 7 \frac{7}{3} - 6)

Graph

Popular Examples

extreme f(x)= x/(x^2+9),-5<= x<= 5 extreme points

f (x) = \frac{x}{x ^{2} + 9}, - 5 \leq x \leq 5

extreme f(x,y)=4x^2+5xy+5y^2 extreme points

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

extreme f(x,y)=5x^2+6y^2-10x-12y+14 extreme points

f (x, y) = 5 x^{2} + 6 y^{2} - 10 x - 12 y + 14

extreme-2x^2y+6x^2+4y^2-16y+16 extreme points

- 2 x^{2} y + 6 x^{2} + 4 y^{2} - 16 y + 16

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

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3-7x-6 ?
The extreme f(x)=x^3-7x-6 is