The graph of a function is given. Choose the answer that represents the graph of its derivative
-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 represents its rate of change at each point. Therefore, the derivative is positive where the original function is increasing, negative where the original function is decreasing, and zero at any local maxima or minima. Looking at the graph, we can see that the derivative should be positive on the intervals (a, b) and (c, d), negative on the interval (b, c), and zero at the local maximum and minimum points. Choice C is the only graph that satisfies these conditions.

The Graph of a Function Is Given