- You should know how to find points of inflection.
E.Applications of Derivatives- You should be able to sketch a curve using first and second derivatives and be able to analyze
the critical points. - You should be able to solve Optimization problems (Max/Min problems), and Related Rates
problems. - You should be able to find the derivative of the inverse of a function.
- You should be able to solve Rectilinear Motion problems.
F.Computation of Derivatives- You should be able to find the derivatives of Trig functions, Logarithmic functions, Exponential
functions, and Inverse Trig functions.
III.Integral Calculus
A.Riemann Sums- You should be able to find the area under a curve using left, right, and midpoint evaluations and
the Trapezoid Rule. - You should know the fundamental theorem of calculus:
f(x) dx = F(b) − F(a)B.Applications of Integrals- You should be able to find the area of a region, the volume of a solid of known cross-section,
the volume of a solid of revolution, and the average value of a function. - You should be able to solve acceleration, velocity, and position problems.
C.Fundamental Theorem of Calculus- You should know the first and second fundamental theorems of calculus and be able to use them
both to find the derivative of an integral and for the analytical and graphical analysis of
functions.
D.Techniques of Antidifferentiation