MAT 1234 Calculus I Section 2.1 Part I Derivatives and Rates of Change

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Presentation transcript:

MAT 1234 Calculus I Section 2.1 Part I Derivatives and Rates of Change

Note WebAssign HW 2.1 I Exam 1 Next Friday. You need to make sure you have an approved calculator.

=2.1? Section 2.1 For the graph of y=f(x), the slope of the tangent line at x=a is (Moving objects) For the position function, y=f(t), the instantaneous velocity at t=a is For a function y=f(x) (without geometric or physical contexts), the instantaneous rate of change at x=a

=2.1?

Section 1.6 We use algebra to compute limits Section 2.6 We compute limits such as the slopes of the tangent line and the instantaneous velocities

=2.1? Section 1.6 We use algebra to compute limits Section 2.1 We compute limits such as the slopes of the tangent line and the instantaneous velocities

Example 1 Find the equation of the tangent line of at

Example 1 The equation of a line pass through is given by

Example 1

Expectations

Example 2 The displacement (in meters) of a particle moving in a straight line is given by where t is measured in seconds. Find the velocity of the particle at t=2

Example 2

Expectations

Classwork and Quiz Do we have 10 minutes for classwork?

Expectations