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Popular >

extreme (x^2-1)/(x^2-9)

Solution

extreme points

\frac{x ^{2} - 1}{x ^{2} - 9}

Solution

Maximum (0, \frac{1}{9})

Solution steps

f^{'} (x) = - \frac{16 x}{( x ^{2} - 9 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{2} - 1}{x ^{2} - 9} : \frac{1}{9}

Maximum (0, \frac{1}{9})

Popular Examples

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

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

extreme x^2+6x-4 extreme points

x^{2} + 6 x - 4

extreme x^2+xy+y^2-19y+120 extreme points

x^{2} + x y + y^{2} - 19 y + 120

extreme g(t)=8t-t^4,-2<= t<= 1 extreme points

g (t) = 8 t - t^{4}, - 2 \leq t \leq 1

extreme f(x)=-0.03x^2+380x-100000 extreme points

f (x) = - 0.03 x^{2} + 380 x - 100000

Frequently Asked Questions (FAQ)

What is the extreme (x^2-1)/(x^2-9) ?
The extreme (x^2-1)/(x^2-9) is Maximum(0, 1/9)