Questions: Match the graph of the function on the right with the graph of its derivative. Choose the correct graph of the function (in blue) and its derivative (in red) below. A. B. C. D.

Solution Steps

• The graph on the right shows a function with a local minimum at \( x = 0 \) and local maxima at \( x = \pm 5 \).

• The derivative of the function should be zero at the local minima and maxima of the function.
• The derivative graph should cross the x-axis at \( x = 0 \) and \( x = \pm 5 \).

• Option A: The red graph (derivative) crosses the x-axis at \( x = 0 \) and \( x = \pm 5 \), matching the critical points of the blue graph (function).

Final Answer