If the function is decreasing, then the derivative is negative, and if the function is increasing, then the derivative is positive. If the function is at a local extremum, then the derivative is zero, and the graph has a horizontal tangent line.[br][br]Check your answer by clicking on the Check Answer checkbox. [br][br]You can check your computation of the slope of the black line by comparing it to the actual slope of the black line. Compare this value to your estimate for m_1.[br][br]You can compare your computation of a symmetric difference quotient against the actual value of a difference quotient with h = 0.5. (Other choices for h can also be good.) Compare this value to your estimate for m_2.[br][br]Compare all of these against the actual value of the derivative, which is the slope of the red tangent line.[br][br]Which of your estimates was closer to the actual derivative? [br]That is going to depend on you. The author of this activity has found that, in practice, it can be challenging to draw a tangent line and find its slope with a great deal of accuracy. Although, your personal skill might contradict this, the symmetric difference quotient where you go to the next available vertical grid line typically gives a better estimate for many students.