1. Problem 1: The graph is given as a function f with a specific shape from x=0 to x=1. (a) To find where f is increasing, look for intervals where the graph moves upwards as x increases. (b) To find where f is decreasing, look for intervals where the graph moves downwards as x increases. (c) For concavity upward, identify intervals where the graph appears curved like a cup 58^. (d) For concavity downward, identify intervals curved like an upside down cup 58. (e) Points of inflection occur where concavity changes, i.e., where the curve shifts from concave up to concave down or vice versa. 2. From the description and sketch for graph 1: - Increasing intervals: From roughly just after the minimum point until near x=1 where it rises steeply. - Decreasing intervals: From x=0 to the local minimum point where the curve dips below -1. - Concave upward intervals: Typically on intervals where the graph bends upwards. Observing the given shape, the initial descent and the final steep rise show concave up. - Concave downward intervals: Intervals where the graph bends downward, such as near the peak after the initial rise. - Inflection points: Occur at the x-values where the curve changes concavity, likely near the peak and near the trough. 3. Repeat for graph 2 with similar reasoning: - Increasing intervals: Where the graph moves upwards. - Decreasing intervals: Where it moves downwards. - Concave upward/downward: Based on the bending of the curve. - Inflection points: Where concavity changes. Detailed numerical intervals require exact graph data, but the step-by-step logic applies. Hence, the answers are: 1(a): Increasing intervals: approximately (around local minimum to 1). 1(b): Decreasing intervals: approximately (0 to local minimum). 1(c): Concave upward intervals: intervals where the curve is shaped like a cup. 1(d): Concave downward intervals: intervals where it bends downward. 1(e): Coordinates at points where concavity changes. 2(a-e) similarly based on graph 2. Please analyze each graph point-by-point using these criteria. q_count:2