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# L10 - x is 6 The position of an object subject only to the...

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L10 – Tangents, Velocities, and Rates of Change Def – The tangent line to y = f ( x ) at the point P ( a, f ( a ) ) is the line through P with slope, if it exists m = 1

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Find the equation of the tangent line to y = x 3 at the point ( 2 , 8 ) . 2
If h = x - a , then m = Find the equation of the tangent line to y = 1 x - 2 at ( 4 , 1 2 ) . 3

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To find the slope of the tangent line to y = 10 - 3 x at x = - 2, at x = 1 3 , and at x = - 5, we can use the general form m = 4
If an object moves along a straight line according to an equation of motion s = f ( t ) where s is displacement (directed distance) from the origin and f ( t ) is the position function, Average velocity = Instantaneous velocity = 5

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Other rates of change: If y is a function of x , and x changes from x 1 to x 2 , then the average rate of change of y with respect to an x on [ x 1 , x 2 ] is Δ y Δ x Instantaneous rate of change of y with respect to

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Unformatted text preview: x is 6 The position of an object subject only to the force of gravity is given by s ( t ) where s is in feet (or meters) and t is in seconds. Initial height is Initial velocity is + if-if 7 A stone is thrown upward with initial velocity 48 ft/sec from a 160 ft tower. a) What is the velocity of the stone at 2 seconds? b) What is the velocity of the stone when it hits the ground? 8 The concentration in mg/min of a certain drug in the bloodstream after t minutes is given in the table. t 5 10 15 20 25 30 35 40 45 50 C ( t ) 6 9 14 21 30 41 53 69 86 105 At what rate is the concentration changing in a) the ﬁrst 5 min b) the last 10 min c) the 50 min period 9...
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L10 - x is 6 The position of an object subject only to the...

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