# 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'