Determine the characteristics of a function (increasing, decreasing, local extrema, concavity, intercepts and inflection points) using a point on the graph and the slope of the graph at that point.
By sliding the point left and right along the graph, determine: 1. The intervals where the function is increasing and decreasing 2. The intervals where the function is concave down (decreasing slopes) and concave up (increasing slopes) 3. The inflection points (points on the graph where the function changes concavity) 4. The local extrema (maximums and minimums) and the values of x at which they occur 5. The x-intercepts (zeros or roots of the function) and the y-intercept.