Skip to main content
\(\newcommand{\dollar}{\$} \DeclareMathOperator{\erf}{erf} \DeclareMathOperator{\arctanh}{arctanh} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)


\(u\)-substitution, Subsection
acceleration, Item
under velocity function, Subsection
area-between, Subsection
average rate of change, Paragraph Section
average value, Subsection
average value of a function, Subsection
chain rule, Paragraph
concavity, Paragraph
concave down, Paragraph
concave up, Paragraph
continuous, Subsection
at \(x = c\), Paragraph
properties, Paragraph
critical number, Paragraph
critical point, Paragraph
critical value, Paragraph
cusp, Item
decreasing, Paragraph Paragraph
definite integral
chain rule, Paragraph
constant function, Paragraph
constant multiple rule, Paragraph
implicit function, Subsection
logarithm, Paragraph Paragraph
power function, Paragraph
product rule, Paragraph
quotient rule, Paragraph
sum rule, Paragraph
differentiable, Item Subsection
evaluating the function, Paragraph
extreme value, Paragraph
extreme value theorem, Paragraph Paragraph
first derivative test, Subsection
function, Subsection
implicit function, Paragraph
piecewise function, Subsection
fundamental theorem of calculus, Subsection
horizontal line test, Subsection
implicit differentiation, Subsection
implicit function, Paragraph
increasing, Paragraph Paragraph
inflection point, Paragraph
input, Subsection
instantaneous rate of change, Paragraph Paragraph
integral sign, Paragraph
integrand, Paragraph
inverse functions, Subsection
Invertible Function, Paragraph
lemniscate, Paragraph
properties, Paragraph Paragraph
limits of integration, Paragraph Paragraph
relative, Paragraph Paragraph
relative, Paragraph Paragraph
natural base, Paragraph
natural logarithm, Paragraph Subsection
net signed area, Paragraph
nth derivative
definition, Paragraph
output, Subsection
parameters, Note
piecewise, Paragraph
product rule, Paragraph
quotient rule, Paragraph
Riemann sum, Paragraph
left, Paragraph
middle, Paragraph
right, Paragraph
second derivative
definition, Paragraph
second derivative test, Paragraph
sigma notation, Paragraph
slope, Subsection
slope-intercept form, Paragraph
tangent line
tangent line approximation, Paragraph
error, Item
The Logarithm, Section
total change theorem, Subsection Subsection
two-parameter, Note