Create a presentation in which you come up with a twice-differentiable function and draw its graph...

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Create a presentation in which you come up with a twice-differentiable function and draw its graph without a calculator by analyzing its properties. You can create a slideshow presentation, a video, or a written report. These properties must be included in a presentation: zeros, symmetry, and first- and second-order derivatives, local and global extreme values, the concavity test, concave up, and concave down. Then, graph the function using a graphing calculator to verify your work. You will submit images of both the hand-drawn graph and the graph on a calculator. Be sure to use precise mathematical language throughout the activity. Create a presentation in which you come up with a twice-differentiable function and draw its graph without a calculator by analyzing its properties. You can create a slideshow presentation, a video, or a written report. These properties must be included in a presentation: zeros, symmetry, and first- and second-order derivatives, local and global extreme values, the concavity test, concave up, and concave down. Then, graph the function using a graphing calculator to verify your work. You will submit images of both the hand-drawn graph and the graph on a calculator. Be sure to use precise mathematical language throughout the activity.