Question

How many inflection point(s) do you see ?

Answer 1

7 inflection points

Explanation:

The given function
`f(x)=sinx+2` has a midline of y=2 where each point of the function that intersects the line is an inflection point. Inflection points are where the concavity changes, defined by when the second derivative is equal to 0 or undefined.

`f(x)=sin(x)+2`

`f'(x)=cos(x)`

`f''(x)=-sin(x)`

`0=-sin(x)`

`x=\pi n` for any integer
`n`

From
`[-10,10]`, there are 7 inflection points, which are
`x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi`

Answer 2

7

Explanation:

There is a point of inflection at each point where the graph crosses the line y=2. There are 7 points of inflection shown.

__

A point of inflection is where the graph changes from being concave downward to concave upward, or vice versa. For a sine function, that is everywhere the function crosses its midline.