Critical Numbers
Extrema
Increasing/Decreasing Functions
Relative Extrema
 Review - Pre-calculus
- Extrema
- Absolute and Relative Extrema (video)
- Interval Notation
- Extrema (video)/Critical Numbers (video) (checkpoints)
- How can extrema be defined for a function?
- How can critical numbers be calculated using derivatives?
- How are critical numbers related to extrema?
- How does Extreme Value Theorem work?
- Increasing/Decreasing Functions (video) (checkpoints)
- How can derivatives be used to find intervals of increasing and decreasing?
- How can derivatives be used to find relative extrema?
Lesson - Challenge 3.3
- Rolle's Theorem
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with equal y-values.
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with equal y-values
- has no point that has a slope of zero
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with equal y-values
- has no point that has a slope of zero
- is continuous
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with equal y-values
- has no point that has a slope of zero
- is continuous from [a, b]
- is differentiable on the interval (a, b)
- Mean Value Theorem
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with unequal y-values.
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with unequal y-values
- has no points with equal to the slope of points a and b
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with unequal y-values
- has no points with equal to the slope of points a and b
- is continuous
- Sketch a graph of a function on a closed interval [a, b] that:
- has endpoints with unequal y-values
- has no points with equal to the slope of points a and b
- is continuous from [a, b]
- is differentiable on the interval (a, b)
- Videos
- Practice
Exit Ticket
- Posted on the board at the end of the block.
Homework
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Standard(s)
- APC.7
- Analyze the derivative of a function as a function in itself.
- Includes:
- comparing corresponding characteristics of the graphs of f, f', and f''
- defining the relationship between the increasing and decreasing behavior of f and the sign of f'
- translating verbal descriptions into equations involving derivatives and vice versa
- analyzing the geometric consequences of the Mean Value Theorem;
- defining the relationship between the concavity of f and the sign of f"; and identifying points of inflection as places where concavity changes and finding points of inflection.
- APC.8
- Apply the derivative to solve problems.
- Includes:
- analysis of curves and the ideas of concavity and monotonicity
- optimization involving global and local extrema;
- modeling of rates of change and related rates;
use of implicit differentiation to find the derivative of an inverse function;- interpretation of the derivative as a rate of change in applied contexts, including velocity, speed, and acceleration; and
differentiation of nonlogarithmic functions, using the technique of logarithmic differentiation.**AP Calculus BC will also apply the derivative to solve problems.Includes:analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration vectors;numerical solution of differential equations, using Euler’s method;l’Hopital’s Rule to test the convergence of improper integrals and series; andgeometric interpretation of differential equations via slope fields and the relationship between slope fields and the solution curves for the differential equations.
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