Question

the graph of the polynomial function f is shown. how many points of inflection does the graph of f have on the given portion of the graph? a one b three c four d five

Explanation:

Step1: Recall inflection - point definition

An inflection point is a point where the concavity of the function changes, i.e., the second - derivative \(f''(x)\) changes sign.

Step2: Observe the graph

Visually inspect the graph of \(y = f(x)\). We look for the points where the curve changes from being concave up (curving upwards like a cup) to concave down (curving downwards like an umbrella) or vice - versa.

Step3: Count inflection points

By observing the given graph of the polynomial function \(f\), we can see that there are three such points where the concavity changes.

Answer:

B. Three