Blog Post 4

Good evening, I'm Alex Falco and I'll be your professor  for this evening's lesson. Today we will be learning how to determine inflection points.

For this lesson we need to remember how to find derivatives so just as a refresher

Find the Derivative:

f(x)= 3x^3+12x^2+72x+5

 by applying some basic rules of finding derivatives we find that the derivative is

f'(x)=9x^2+24x+72

Now that we are refreshed on finding derivatives we can learn how to find inflection points in functions

So what is an inflection point?

An inflection point is anywhere on a function where the curve changes direction

 It looks likes this:



Ok, we now know what an inflection point is and what it looks like. So, how do you find one?

The road to finding inflection points is paved with derivatives. in order to find inflection points we look for spots where the second derivative of a function equals zero.

lets start with a function:


 f(x)=3x^3+2x^2+1

then we find the derivative:


f'(x)= 9x^2+4x

now we find the second derivative by taking the derivative of the first:


f''(x)= 18x+4


With the second derivative found we can find the inflection point by setting our equation equal to zero and solving for x:


18x+4=0
18x=-4
x=(-2/9)

This means that a possible inflection point is located on the x=(-2/9) on our original function

So, to review our steps for finding the location of an inflection point are as follows:

Step 1:
Take the derivative of your function, this is your first derivative

Step 2:
Take the derivative of your first derivative, this is your second derivative

Step 3:
Set the second derivative equal to zero and solve. This answer is the x-value of the inflection point on your original function


congrats you now know how to find inflection points of functions!!