Angles, Radian Measure, and Unit Circle.

Duration of Unit: 15 days

Missouri Learning Standards/ Essential Learning Outcomes from Missouri State University

Section 4.1

4.1.1 Express changing quantities in terms of derivatives.
4.1.2 Find relationships among the derivatives in a given problem.
4.1.3 Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.

Section 4.2

4.2.1 Describe the linear approximation to a function at a point.
4.2.2 Write the linearization of a given function.
4.2.3 Draw a graph that illustrates the use of differentials to approximate the change in a quantity.
4.2.4 Calculate the relative error and percentage error in using a differential approximation.

Section 4.3

4.3.1 Define absolute extrema.
4.3.2 Define local extrema.
4.3.3 Explain how to find the critical points of a function over a closed interval.
4.3.4 Describe how to use critical points to locate absolute extrema over a closed interval.

Section 4.4

4.4.1 Explain the meaning of Rolle’s theorem.
4.4.2 Describe the significance of the Mean Value Theorem.
4.4.3 State three important consequences of the Mean Value Theorem.

Section 4.5

4.5.1 Explain how the sign of the first derivative affects the shape of a function’s graph.
4.5.2 State the first derivative test for critical points.
4.5.3 Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function’s graph.
4.5.4 Explain the concavity test for a function over an open interval.
4.5.5 Explain the relationship between a function and its first and second derivatives.
4.5.6 State the second derivative test for local extrema.

Section 4.6

4.6.1 Calculate the limit of a function as increases or decreases without bound.
4.6.2 Recognize a horizontal asymptote on the graph of a function.
4.6.3 Estimate the end behavior of a function as increases or decreases without bound.
4.6.4 Recognize an oblique asymptote on the graph of a function.
4.6.5 Analyze a function and its derivatives to draw its graph.

Section 4.7

4.7.1 Set up and solve optimization problems in several applied fields.

Section 4.8

4.8.1 Recognize when to apply L’Hôpital’s rule.
4.8.2 Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
4.8.3 Describe the relative growth rates of functions.

Section 4.9

4.9.1 Describe the steps of Newton’s method.
4.9.2 Explain what an iterative process means.
4.9.3 Recognize when Newton’s method does not work.
4.9.4 Apply iterative processes to various situations.

Section 4.10

4.10.1 Find the general antiderivative of a given function.
4.10.2 Explain the terms and notation used for an indefinite integral.
4.10.3 State the power rule for integrals.
4.10.4 Use antidifferentiation to solve simple initial-value problems.

Big Idea of the Unit:
Integrate various functions.

Specific Assessment Evidence:

The assessment will be a paper & pencil test. It could be comprised of multiple-choice, matching, and/or fill in the blank. Most of the points in this assessment will come from the multi-step problems.

Math Resources
Link to the Missouri Learning Standards
DESE Math Curriculum and Instruction Homepage