The learner will be able to understand derivatives
graphically, numerically, and analytically.
The learner will be able to interpret derivatives
as a rate of change.
The learner will be able to define derivatives as
a limit.
The learner will be able to relate
differentiability and continuity.
The learner will be able to calculate the slope of
a curve at a point (including vertical tangents).
The learner will be able to explain find tangent
lines and approximations.
The learner will be able to use limits of the average
rate of change to find instantaneous rates of change.
The learner will be able to approximate
derivatives from graphs and tables.
The learner will be able to relate functions and
their derivatives.
The learner will be able to use and interpret the
Mean Value Theorem.
The learner will be able to use the derivative to
find increasing and decreasing intervals of functions.
The learner will be able to use the second
derivatives to explore concavity.
The learner will be able to apply derivatives to
solving a variety of problems including related rates and optimization.
The learner will be able to find derivatives of
sums, differences, products, and quotients and use the chain rule.
The learner will be able to find the derivatives
of all the basic functions (including parametric, polar and vector .
The learner will be able to differentiate
implicitly.
The learner will be able to use Euler’s method for
approximations of differential equations
The learner will be able to use L’Hospital’s rule to evaluate limits.
