1. If a stone is thrown down at 120 feet per second from a height of 1,020 feet,
ID: 2831594 • Letter: 1
Question
1. If a stone is thrown down at 120 feet per second from a height of 1,020 feet, its height after t seconds is given by s(t) = 1,020 ? 120t ? 16t2.
a.Find its instantaneous velocity function. v(t) =
b.Find its velocity at time t = 3.
v(3) =
2. Compute the indicated derivative.
L(r) = ?1.04r + 5.5; L'(3.1)
L'(3.1) =
3.Compute the derivative function f(x) =
3x/k-b (k ? 0)
4. Compute the indicated derivative.
U(t) = 5.1t2 + 5.1; U'(8)
5.Compute the derivative function f(x) algebraically.
f(x) = x2 ? 2
6.Compute f(x) algebraically for the given value of a.
f(x) = x ? 9x3; a = 1
f(a) =
7.Find the equation of the tangent to the graph at the indicated point.
f(x) = 8x + 1; a = 2
8.Compute f '(a) algebraically for the given value of a.
f(x) = 3x2 + x; a = ?5
9.Compute the indicated derivative.
U(t) = 5.5t2 ? 1.6t; U'(3)
U'(3) =
10.Compute the derivative function f(x) algebraically.
f(x) = ?5x + 5
f(x) =
11.The following chart shows annual per capita sales of bottled water in the United States for the period 2000?2010.
a. The functionR(t) = ?0.18t2+ 3t + 15 gallons (0 ? t ? 10) gives a good approximation, where t is time in years since 2000. Find the derivative function R'(t).
R'(t) =
b. According to the model, how fast were per capita sales of bottled water changing in 2010?
Per capita sales of bottled water were decreasing at a rate of ??
12.Compute the derivative function f(x) algebraically.
f(x) = ?4x ? 9x2
f(x) =
13.Find the equation of the tangent to the graph at the indicated point.
f(x) = x2 ? 6x; a = ?7
14.
Find the equation of the tangent to the graph at the indicated point.
f(x) = x2 ? 1; a = 5
y =Explanation / Answer
1) v(t) = -120 -32t; v(3) = -216;
2) L'(3.1) =-1.04
3) 3/(k-b) ;
4) U(8) = 81.6;
5) f'(x) = 2x
6) f(a=1) = -8;
7) y = 8x+1;
8) f'(a) = -29 ; a =5
9) U'(3) = -31.4;
10) f'(x) = -5;
11) a) R'(t) = -0.36t+3; b) R'(10) = -0.6;
12) f'(x) = -4 -18x;
13) y = -20x-49;
14) y = 10x -5
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