Everything You Need to Know About Sketching Curves Using Derivatives
The first and second derivative tests are pivotal tools in calculus for analyzing the behavior of functions. They assess where functions increase or decrease, identify local extrema, and determine concavity. While the first derivative reveals increasing or decreasing trends and locates potential extrema, the second derivative offers insights into the function’s concavity, indicating whether a […]
Differentiability: Everything You Need To Know
Differentiability and Smoothness: A function is differentiable at a point if it is “smooth” (without sharp corners or cusps) and continuous at that point. The smoothness implies that the function’s graph can be approximated by a tangent line at every point where the function is differentiable. Differentiability and Continuity: While differentiability implies continuity, the converse […]
