Tangent Lines & Rates of Change

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Presentation transcript:

Tangent Lines & Rates of Change AP Calculus September 16, 2016 Mrs. Agnew

Essential Stuff Essential Question How do you find the equation of a tangent line to a curve? Essential Vocabulary Secant Line Tangent line Instantaneous Rate of Change

Tangent Line Problem From our initial discussion of calculus, we identified two major problems to solve using differentiation: The Tangent Line Problem The Velocity Problem We have examined these problems numerically. We will now solve these problems algebraically using Differential Calculus.

The Tangent Line Problem Line intersects curve at one point Cannot find slope when given one point Recall that the slope of a line is the difference in the y values over the difference in the x values. Using a diagram & secant lines, we can develop a formula for the slope of a tangent line at x = a.

Slope of the Tangent Line The Slope of the Tangent Line at x = a *The slope of the tangent line is also referred to as the slope of the curve.

Examples… Find the equation of the line tangent to the curve at the point (1, 1). Find the equation of the line tangent to the curve at the point (1, 3 2 ). Find the equation of the line tangent to the curve at the point (3, 1).

HW: September 16, 2015 Guided Practice Homework (Stewart) Stewart - page 149 #15, 16, 17, 23(a, b) Homework (Stewart) Worksheet on Tangent Lines Page 148 – 149 #7, 8, 12(a, b), 13, 18, 22(a,b), 25