Download AP Calculus BC FR: FTC Practice Name: 11-18

AP Calculus BC
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1.
FR: FTC Practice Name:
11-18-15
Let f be a differentiable function, defined for all real numbers x, with the following properties.
(ii)
f (x)  ax 2  bx
f (1)  6 and f (1)  18
(iii)

(i)
2
1
f (x)dx  18
Find f (x) . Show your work.
2.
Let f be a function such that f (x)  6x  8 .
(a)
Find f (x) if the graph of f is tangent to the line 3x  y  2 at the point (0, -2).
(b)
3.
Find the average value of f (x) on the closed interval [-1, 1].
Let f be the function that is defined for all real numbers x and that has the following properties.
(i)
(ii)
(iii)
(a)
f (x)  24x  18
f (1)  6
f (2)  0
Find each x such that the line tangent to the graph of f at (x, f (x)) is horizontal.
(b)
(c)
4.
Write an expression for f (x) .
Find the average value of f on the interval 1  x  3 .
Let f and g be continuous functions with the following properties.
(i)
g(x)  A  f (x) where A is a constant
(ii)

2
(iii)

3
1
2

3
f (x)dx 

3
2
g(x)dx
f (x)dx  3A
(a)
Find
(b)
Find the average value of g(x) in terms of A over the interval [1, 3].
1
f (x)dx in terms of A.
(c)
Find the value of k if

1
0
f (x  1)dx  kA .