Question

How many inflection point(s) do you see ?

Answer 1

Answer:

  7

Step-by-step 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.

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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.

Answer 2

Answer:

7 inflection points

Step-by-step 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$x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi$