Question

question 6 (1 point) retake question
the following is a graph of the first derivative of the function ( f(x) ). on which of the following intervals is ( f(x) ) concave down?

Explanation:

Step1: Recall the concavity rule

The function \(y = f(x)\) is concave down when \(f''(x)<0\). Since the given graph is of \(y = f'(x)\), \(f''(x)\) is the slope of \(y = f'(x)\).

Step2: Analyze the slope of \(y = f'(x)\)

Looking at the graph, the slope of \(y = f'(x)\) (i.e., \(f''(x)\)) is negative in the interval from the \(x -\)coordinate of point \(C\) to the \(x -\)coordinate of point \(F\).

Answer:

The function \(f(x)\) is concave down on the interval where the slope of the first - derivative graph (given graph) is negative.