Building enduring mathematical understanding requires understanding the why and how of mathematics in addition to mastering the necessary procedures and skills. To foster this deeper level of learning, AP Calculus AB is designed to develop mathematical knowledge conceptually, guiding students to connect topics and representations throughout the course and to apply strategies and techniques to accurately solve diverse types of problems.
By the end of the course students should be able to:
A normal line to the graph of a function f at point (x,f(x)) is the line perpendicular to the tangent line at the same point. An equation of the normal line to the curve y=2x^3+x at the point where x=2 is______?
The position s(t) of a particle on the x-axis at time t, t > 0, is cos t. The average velocity of the particle for 0≤t≤pi/2 is __________?