TBIL-Cal Applications of Derivatives (AD)

Chapter 3 Applications of Derivatives (AD)

How can we use derivatives to solve application questions?

By the end of this chapter, you should be able to...

Use derivatives to answer questions about rates of change and equations of tangents.
Use tangent lines to approximate functions.
Model and analyze scenarios using related rates.
Use the Extreme Value Theorem to find the global maximum and minimum values of a continuous function on a closed interval.
Determine where a differentiable function is increasing and decreasing and classify the critical points as local extrema.
Determine the intervals of concavity of a twice differentiable function and find all of its points of inflection.
Sketch the graph of a differentiable function whose derivatives satisfy given criteria.
Apply optimization techniques to solve various problems.
Compute the values of indeterminate limits using L’Hôpital’s Rule.

Before beginning this chapter, you should be able to...

Find the derivative of a function using methods from Section 2.3, Section 2.4, Section 2.5, and Section 2.6.
Find the second derivative of a function. (Khan Academy
¹
www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-6/a/second-derivatives-review
)
Determine whether values are in the domain of a function (Khan Academy
²
www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:determining-the-domain-of-a-function/v/determine-values-domain
)
Find local and global extrema given the graph of a function (Khan Academy
³
www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:maximum-and-minimum-points/v/identifying-relative-and-absolute-maxima-and-minima
)
Find the intervals where a graph is increasing or decreasing (Khan Academy
⁴
www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:intervals-where-a-function-is-positive-negative-increasing-or-decreasing/v/increasing-decreasing-positive-and-negative-intervals
)
Determine the zeros of a polynomial (Khan Academy
⁵
www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/polynomial-zeros-introduction
)
Modeling with multiple variables (Khan Academy
⁶
www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:modeling/x2ec2f6f830c9fb89:modeling-with-multiple-variables/v/modeling-with-multiple-variables-pancakes
)