Question

What is the x-coordinate of the point of inflection on the graph of `y= 1/10x^5`?

Answer 1

At x = 0 there is a point of inflection.

Explanation:

Find the second derivative.
`dy/dx` = `(5/10)x^4`
`(d^2y)/dx^2` = `(20/10)x^3`= `2x^3`

Make 2nd derivative equal to 0. Solve it for x. You are doing this to find for what value of x the function has point of inflection.
`2x^3`=0
x = 0

graph{(1/10)x^5 [-11.25, 11.25, -5.63, 5.62]}