Question

What are the coordinates of the point of inflection on the graph of `y=x^3-15x^2+33x+100`?

Answer 1

(5,15)

Explanation:

To find the inflection point, you will need to take the second derivative.

`y=x^3-15x^2+33x+100`

`y'=3x^2-30x+33`

`y''=6x-30`

`6x=30`

`x=5`

Now that you have your `x`, plug it into your first equation:

`y(5)=(5)^3-15(5)^2+33(5)+100`
`=125-375+165+100=15`
The inflection point is (5,15)