1.Find the slope of the tangent lines to the curve f(x) x^2-9 at the points wher

Question

1.Find the slope of the tangent lines to the curve f(x) x^2-9 at the points where x = -2, 1, and 2

2.experiment on an object suggest that it will fall approximately 16.4t^2 feet in t seconds

( round to the nearest tenth for all your answers)

a. how far will it fall betweeen t=1 and t=2 ?

b. how far will it fall betweeen t=2 and t=3 ?

c. what is the average velocity on the interval 3<=t<=4 ?

d. what is the average velocity on the interval 4<=t<=4.01 ?

e. The object's instataneosly velocity at t = 4

Explanation / Answer

1. slope at x is d(f(x))/dx =   2x
   Hence, at x = -2, slope = -4
               at x = 1, slope = 2
               at x = 2, slope = 4

2. a) 16.4*(4-1) = 49.2
    b) 16.4*(9-4) = 82
    c) avg. velocity = [ 16.4*(16-9) ] / 1
                          = 114.8
    d) avg. velocity = [ 16.4*(4.012 - 42 ) ] / 0.01
                          = [ 16.4*8.01*0.01 ] / 0.01
                          = 131.364
    e) inst. velocity = 2*16.4*4
                           = 131.2

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