How do you describe the concavity of the graph and find the points of inflection (if any) for #f(x) = x^3 - 3x + 2#?
1 Answer
Oct 18, 2015
The function has a minimum at >
The function has a maximum at >
Explanation:
Given -
#y=x^3-3x+2#
#dy/dx=3x^2-3#
#(d^2x)/(dx^2)=6x#
#dy/dx=0 => 3x^2-3=0#
#3x^2=3#
#x^2=3/3=1#
#sqrt(x^2)=+-sqrt1#
#x=1#
#x=-1#
At >
#(d^2x)/(dx^2)=6(1)=6>0#
At >
Hence the function has a minimum at >
At >
#(d^2x)/(dx^2)=6(-1)=-6<0#
At >
Hence the function has a maximum at >
graph{3x^3-3x+2 [-10, 10, -5, 5]}
Watch this lesson also'on Maxima / Minima'