Question

you are given the following graph of the function f(x):
find the point where the second derivative changes sign from negative to positive?
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Explanation:

Step1: Recall the property of inflection point

The second - derivative \(f''(x)\) changes sign at an inflection point. If \(f''(x)\) changes from negative to positive, the function \(f(x)\) changes from concave down to concave up.

Step2: Analyze the concavity from the graph

Looking at the graph of \(y = f(x)\), we observe the concavity. The point where the concavity changes from concave down (where \(f''(x)<0\)) to concave up (where \(f''(x)>0\)) is the point of interest. By visual inspection of the given graph of the function \(y = f(x)\), we can see that the function changes its concavity at \(x = 2\).

Answer:

\(x = 2\)