Code Scholars Tutoring · AP Calculus BC
7 topics across 4 lessons, with explanations, worked examples, and self-checks that develop complete mathematical reasoning.
Topics 4.1, 4.2, 4.3
A derivative measures an instantaneous change in one quantity per unit of another. Velocity is the derivative of position, acceleration is the derivative of velocity, and speed is the magnitude of velocity. A particle speeds up where velocity and acceleration have the same nonzero sign. Interpret a second derivative using squared input units and describe average versus instantaneous rates accurately.
Topics 4.4, 4.5
Name every time-dependent quantity and write a geometric or physical relationship valid throughout the motion. Differentiate with respect to time before substituting the instantaneous values. Keep signs on given rates and solve for the requested rate. A diagram helps distinguish changing distances from fixed dimensions.
Topics 4.6
The tangent line provides a local approximation near a point with known function and derivative values. The differential estimates output change from input change. Concavity determines whether the tangent estimate is above or below the true value locally. An estimate is most useful near the base point; carry the input change with its sign.
Topics 4.7
Before applying L’Hospital’s rule, verify that the quotient approaches or an infinite-over-infinite form, and that the differentiability and denominator-derivative conditions hold on the relevant punctured interval. Replace the quotient by the quotient of derivatives when the theorem applies. Other forms need algebraic rewriting first. Recheck the form before applying the rule again.
