Answer:
the graph of f has 3 turning points
Explanation:
The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.
Derivative
The derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.
Turning Point
Where the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.
The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.
3 Crossings
If the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.
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Additional comment
In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.