Question

question consider the image below. which linear function gives the slopes of the tangent lines of the quadratic function? select the correct answer below: a (red) b (black) c (blue) d (green)

Explanation:

Step1: Recall tangent - slope concept

The slope of the tangent line to a function at a point represents the instantaneous rate of change of the function at that point. For a quadratic function, the derivative gives the formula for the slope of the tangent lines at different points. The derivative of a quadratic function is a linear function.

Step2: Analyze the graph

We need to find the linear function that represents the slopes of the tangent lines of the quadratic function. The slope of a line is given by \(m=\frac{\Delta y}{\Delta x}\). A linear function that represents the slopes of the tangent lines of a quadratic will have a constant rate of change. By observing the graph, we can see that the red - line (a) has the correct behavior as it can represent the changing slopes of the tangent lines of the quadratic function.

Answer:

A. a (red)