Home > Calculus > Determining Points of Inflection for a Function

How do you find the inflection points of the graph of the function #f(x) = x^3 - 3x^2 + 3x#?

Answer 1

Ezra Adams

Find the points on the graph where the concavity changes.

#f(x) = x^3 - 3x^2 + 3x#.

So, #f'(x) = 3x^2 - 6x + 3#.

And #f''(x) = 6x - 6#.

#f''(x)=0# for #x=1#. Testing on each side of #1# we find that

#f''(x) < 0# (so the graph of #f# is concave down) for #x<1# #f''(x) > 0# (so the graph of #f# is concave up) for #x>1#

At #x=1#, we have #y=f(1)=3-3+1=1#.

The inflection point is #(1, 1)#.

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Answer 2

Christopher Agresta

You must study your second derivative:

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Answer 3

Isaiah Allen

To find the inflection points of ( f(x) = x^3 - 3x^2 + 3x ), you need to find the second derivative of the function, ( f''(x) ), set it equal to zero, and solve for ( x ). Then, substitute those values of ( x ) back into the original function to find the corresponding ( y )-coordinates. Finally, state the coordinates of the inflection points as ( (x, f(x)) ).

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Answer from HIX Tutor

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