Transcript AP Calculus BC – 3.6 Chain Rule 1

AP Calculus BC – Chapter 6
Differential Equations and Mathematical Modeling
6.1: Antiderivatives and Slope Fields
Learning Objectives: Students will/I can…
Construct antiderivatives using the Fundamental Theorem of
Calculus.
Find antiderivatives of polynomials, ekx, and selected trigonometric
functions of kx, as well as linear combinations of these functions.
Solve initial value problems of the form dy/dx = f(X),
y0 = f(x0).
Construct slope fields using technology and interpret slope fields as
visualizations of differential equations.
Mathematical Practice:
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Look for and make use of structure.
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Mathematically proficient students look closely
to discern a pattern or structure.
AP Calculus BC Standards
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Integrals:
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Applications of antidifferentiation.
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Finding specific antiderivatives using initial conditions,
including applications to motion along a line.
Quote of the Day:
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“…regarding the fundamental
investigations of mathematics, there is
no final ending…no first beginning.”
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Felix Klein( 1849 - 1925)
Warm Up:
1.
Find all functions y that satisfy
dy/dx = sec2 x + 2x + 5.
2.
Find the particular solution to the
equation dy/dx = ex – 6x2, with
y(1) = 0.
Some examples:
1. Find the particular solution to the
equation dy/dx = 2x – sec2x whose
graph passes through the point (0, 3).
2. Find the solution to the differential
equation f’(x) = e-x2 for which f(7) = 3.
3. Graph the family of functions that
solves the differential equation
dy/dx = cos x.
Assignment:
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HW 6.1A:
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Quick Review
Group Activity Exploration Worksheet
Read Lesson 6.1.