Question

the graph of the function f is shown below. if m is the slope of the line tangent to the graph of f at x = 6, which statement best describes the value of m?

Explanation:

Step1: Recall tangent - slope concept

The slope of the tangent line to the graph of a function \(y = f(x)\) at a point \(x=a\) is equal to the derivative of the function at that point, \(m = f^{\prime}(a)\). We can estimate the slope by looking at the steepness of the curve at \(x = 6\).

Step2: Analyze the graph at \(x = 6\)

At \(x = 6\), the function \(y=f(x)\) is increasing. A function that is increasing has a positive - valued derivative. The tangent line to the curve at \(x = 6\) has a positive slope.

Answer:

\(m>0\)