AP Calculus AB · Summary

Unit 4 summary

1. A derivative’s units are output units per input unit. Interpret it by naming the quantity, the moment, the rate with units and the direction.
2. From a table, estimate a derivative with the difference quotient over the two listed inputs closest to the point, one on each side.
3. Velocity is $x'(t)$, acceleration is $v'(t)$ and speed is $|v(t)|$. A particle changes direction where $v$ changes sign.
4. Speed increases when velocity and acceleration have the same sign and decreases when their signs are opposite.
5. For related rates: write the equation linking the quantities, differentiate with respect to time, then substitute the values for that moment.
6. The tangent line $L(x) = f(a) + f'(a)(x - a)$ underestimates where the graph is concave up and overestimates where it is concave down.
7. Use L’Hôpital’s rule only on $\frac{0}{0}$ or $\frac{\infty}{\infty}$ forms, differentiating the top and the bottom separately.