Dictionaries 1 3 3 X 2

If # f(x) = x^3 - 6x^2 + 9x +1#, what are the points of inflection, concavity and critical points?

• Dictionaries 1 3 3 X 2
• Dictionaries 1 3 3 X 27

1 Answer

Here, the critical points are
#(1,5), 'where the slope is zero'#
#' and curvature is negative, thus being a maximum'##' representing concave down'#

Fasttasks 2 53 km. #(3,1), 'where the slope is zero'#
#' and curvature is positive, thus being a minimum '##'representing concave up'#

Here, the critical points are (1,5), 'where the slope is zero' ' and curvature is negative, thus being a maximum' representing concave down' (3,1), 'where the slope is zero' ' and curvature is positive, thus being a minimum 'representing concave up' However, the point (2,3), 'where the curvature is zero' ' and curve is changing from concave down to concave up'known as point of inflection. For multiplication, use the. symbol. A. symbol is not necessary when multiplying a number by a variable. For instance: 2. x can also be entered as 2x. Similarly, 2. (x + 5) can also be entered as 2(x + 5); 2x. (5) can be entered as 2x(5). The. is also optional when multiplying with parentheses, example: (x + 1)(x - 1). Order of Operations.

However, the point
#(2,3), 'where the curvature is zero'#
#' and curve is changing from concave down to concave up'##'known as point of inflection'#

Explanation:

#'Given:'#

Maya 2016 sp4 – professional 3d modeling and animation tool. #f(x)=x^3-6x^2+9x+1#

#f'(x)=3x^2-12x+9#

#'Solving for x where f'(x)=0,'#

#3x^2-12x+9=0#

#'Dividing by 3'#

#x^2-4x+3=0#

#x^2-3x-1x+3=0#

#x(x-3)-1(x-3)=0#

#(x-1)(x-3)=0#

#x=1, x=3. 'form the points where the slope is zero'#

#f'(x)=3x^2-12x+9#

#f'(x)=6x-12#

#'Solving for x where f'(x) is zero'#

#6x-12=0#

#6(x-2)=0#

#x-2=0#

#x=2. 'form the point where the curvature is zero.'#
#'The point where the curvature changes its sign'#

#x=2, 'forms a point of inflexion'#

#x=1, 'the curvature is', #
#6x-12=6xx1-12=6-12=-6#

#x=3, 'the curvature is', #
#6x-12=6xx3-12=18-12=+6#

#'From x=1, to x=2, the curvature is negative'#
#' indicating concave down'#

#'From x=2, to x=3, the curvature is positive'#
#' indicating concave up'#

The function takes the values as evaluated below

#f(x)=x^3-6x^2+9x+1#

#f(1)=(1)^3-6(1)^2+9(1)+1=1-6+9+1=-5+10=5#

#f(2)=(2)^3-6(2)^2+9(2)+1=8-24+18+1=-16+19=3#

#f(3)=(3)^3-6(3)^2+9(3)+1=27-54+27+1=-27+28=1#

Here, the critical points are
#(1,5), 'where the slope is zero'#
#' and curvature is negative, thus being a maximum'##' representing concave down'#

#(3,1), 'where the slope is zero'#
#' and curvature is positive, thus being a minimum '##'representing concave up'#

However, the point
#(2,3), 'where the curvature is zero'#
#' and curve is changing from concave down to concave up'#

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