# What are the local extrema of #f(x)= (3x^3-2x^2-2x+43)/(x-1)^2+x^2#?

##### 1 Answer

#### Answer:

Minima f : 38.827075 at x = 4.1463151 and another for a negative x. I would visit here soon, with the other minimum..

#### Explanation:

In effect, f(x )= (a biquadratic in x)/

Using the method of partial fractions,

This form reveals an asymptotic parabola

As

The first graph reveals the parabolic asymptote that lies low.

The second reveals the graph on the left of the vertical asymptote, x

= 1, and the third is for the right side. These are befittingly scaled to

reveal local minima f = 6 and 35, nearly Using a numerical iterative

method with starter

x =4.1473151, nearly. I would get soon, the

graph{(x^2+3x+4+3/(x-1)+42/(x-1)^2-y)(x+.0000001y-1)(y-x^2-3x-4)=0 [-10, 10, 0, 50]}

graph{(x^2+3x+4+3/(x-1)+42/(x-1)^2-y)(x+.0000001y-1)=0 [-10, 10, -10, 10]}

graph{(x^2+3x+4+3/(x-1)+42/(x-1)^2-y)(x+.0000001y-1)=0 [0, 10, 0, 50]}