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# 2413labI4 - Laboratory I.4 Explorations with the Slopes of...

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Laboratory I.4 Explorations with the Slopes of Tangents Goals • Students will reinforce lecture concepts about the relationship between slopes of secant lines and slopes of tangent lines. • Students will understand why some functions do not have tangent lines at certain points. Before the Lab As you've seen in lecture, the slope of the tangent line depends on the limit of slopes of secant lines. In this lab, we're going to ask you to draw secant lines. Here's some background algebra to help you do it more efficiently in DERIVE. The secant line goes through two points of the graph of a function f ( x ). The first point is the point at which you're trying to find the derivative; let's call that point ( c , f ( c )). The second point is a small distance h away: ( c + h , f ( c + h )). So the slope of the line between these two points is h c f h c f c h c c f h c f x y ) ( ) ( ) ( ) ( ) ( + = + + = Δ Δ and the point-slope formula for the secant line, y, with that slope through the point ( c , f ( c )) is ) ( ) ( ) ( ) ( ) ( ) ( c x h c f h c f c f c x x y x f y + + = Δ Δ + =

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MATH 2413 Lab 4 Page 2 of 3 In the Lab (80 pts) 0. In this first section, we will set up some general formulas that will work with any function you might care to use in DERIVE. You will apply them in the later sections. Author f(x) := (yes, this is blank after the = sign) This lets DERIVE know that the letter f will stand for a function, not an ordinary variable. Author
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2413labI4 - Laboratory I.4 Explorations with the Slopes of...

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