The graph of a function is given. Choose the answer that represents the graph of its derivative
-

Question

Quizplus · Accepted Answer

The derivative of a function gives the slope of the tangent line to the graph of the function at each point. Looking at the given graph, we can see that the slope of the tangent line is zero at the local maxima and minima (where the graph changes direction) and becomes more negative or positive as we move away from these points. This means that the derivative of the function is zero at the local maxima and minima, and becomes increasingly negative or positive as we move away from these points. Therefore, the graph of the derivative should cross the x-axis at the local maxima and minima and be negative to the left of these points and positive to the right of these points. Choice B is the only graph that satisfies these conditions.

The Graph of a Function Is Given