Now if we substitute x = 2, we get
= 4 + 2 +
Solving for y, we get
y = ±
- A In order to find the inflection point(s) of a polynomial, we need to find the values of x where
its second derivative is zero.
First, we find the second derivative.
= 20x^3 − 5x^4
= 60x^2 − 20x^3
Now, let’s set the second derivative equal to zero and solve for x.
60 x^2 − 20x^3 = 0
20 x^2 (3 − x) = 0
x = 3
This is the point of inflection. x = 0 is not a point of inflection because does not change
sign there.
You can use a calculator on this part of the exam, and you can use it to find the inflection
point(s) of this graph.
Graphing Calculator (TI-83 and TI-84)
Press the Y= button, and enter the following values to the list:
Y 1 = 5X^4 − X^5
