Enter points such as inflection points in ascending order ie

Enter points, such as inflection points in ascending order, i.e. smallest x values first. Enter intervals in ascending order also.

The inflection point for this function is.

3-5 #2

Answer the following questions for the function defined on the interval. Enter points, such as inflection points in ascending order, i.e. smallest x values first. Enter intervals in ascending order also. The functionhas vertical asympototes atand. is concave up on the regiontoandto. The inflection point for this function is.

Solution

x = +6 ; x = -6 (denominator roots) y\' = [(3x^2) (x^2-36)-(x^3)(2x)]/(x^2-36)^2 y\' = (3x^4 - 27 x^2 - 2 x^4)/(x^2-36)^2 y\' = x^2(x^2-27)/(x^2-36)^2 critical point x =- 3v3 ; x = + 3v3 y\'\' = [(4 x^3 - 54 x)(x^2-36)^2 - (x^4- 27 x^2)*2(x^2-36)(2x)]/(x^2-36)^4 y\'\' = 4 x [(x^2 - 27/2)(x^2-36) - (x^4-27x^2)]/(x^2-36)^3 y\'\' = 4 x [-(27/2)x^2 - 36 x^2 + 243/2 + 27 x^2]/(x^2-36)^3 Y\'\' = 4 x( (9/2) x^2 + 243/2)/(x^2-36)^3 Inflection point x =0 ( - 15 ; -6) concave x =- 3v3 maximum (-3;0) convexe (0,+3) concave (+3,+15) convexe x = + 6v3 minimum