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Popular >

extreme (x^2-5)/(x-3)

Solution

extreme points

\frac{x ^{2} - 5}{x - 3}

Solution

Maximum (1, 2), Minimum (5, 10)

Solution steps

f^{'} (x) = \frac{x ^{2} - 6 x + 5}{( x - 3 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Decreasing

: 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 1

into

\frac{x ^{2} - 5}{x - 3} : 2

Maximum (1, 2)

Plug

x = 5

into

\frac{x ^{2} - 5}{x - 3} : 10

Minimum (5, 10)

Maximum (1, 2), Minimum (5, 10)

Popular Examples

inflection 3x^{2/3}-2x inflection points

3 x^{\frac{2}{3}} - 2 x

inverse of f(x)=(x-7)/(x+1)inverse

f (x) = \frac{x - 7}{x + 1}

range of f(x)=((8x-3))/x range

f (x) = \frac{( 8 x - 3 )}{x}

domain of f(x)= x/(sqrt(25-x^2))domain

f (x) = \frac{x}{25 - x ^{2}}

f (x) = x^{2}

Frequently Asked Questions (FAQ)

What is the extreme (x^2-5)/(x-3) ?
The extreme (x^2-5)/(x-3) is Maximum(1,2),Minimum(5,10)