This set of 20 task cards is divided into 5 different sets of 4 cards.
Cards 1-4: Students are given different information about the function, its derivative, and its second derivative. From the information the students should draw a sketch. The solutions show a possible sketch of the function and also a list of how the collected data was used to complete the sketch.
Cards 5-8: Students are given graphs of the derivative of a function. Students are asked to draw a sketch of the function. The solutions show sketches of the function and a list of statements used to complete the graph.
Cards 9-12: Students are given charts of information about the sign of the derivative, the graph of the derivative, the sign of the second derivative. They are asked to draw a sketch of the original function from the given information. The solutions show sketch of the original function and a list of statements that led to the sketch.
Cards 13-16: Students are given a algebraic expression for the derivative of a function. Students must describe where the graph of the original function is increasing, decreasing, has a slope of zero, where the original function is concave up and concave down, and any point of inflection. Then students are asked to draw a sketch of the original function.
Cards 17-20: Students are given an algebraic expression for the derivative of a function. Students are asked to locate the x values where the absolute minimum and maximum occur, draw a sketch of the original function, and show the absolute minimum and maximum on the sketch.
Using the special student recording sheet students can display their solution to each question. Upon completing their solution, the student can then use a QR reader to scan the QR code. The students will be shown a complete solution to the question. Students could study these solutions to learn how to better solve the question.