Curve sketching

Curve sketching is the process of drawing a graph of a function based on analyzing its shape and key features. It involves examining where the function increases or decreases, points where it reaches a maximum or minimum, and where it bends or levels off. By studying derivatives, one can identify slopes and concavity, helping to understand the curve's behavior. This systematic analysis allows for an accurate representation of the function's overall form without needing to plot every point, making it a valuable tool for visualizing complex mathematical relationships in a clear and informative way.