The Fundamental Theorem Of Calculus Worksheet Page 3
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9Calculus Maximus
WS 4.3: The FTOC
Short Answer
7. Let f be a function such that
f
x
6
x
12
.
(a) Find
f x if the graph of f is tangent to the line 4
at the point
0, 5
x y
5
(b) Find the average value of
f x on the closed interval
1,1
.
. Which of the following
8. Suppose f has a negative derivative for all values of x and that
f
1
0
statements must be true of the function
x
h x
f t dt
?
0
Give reasons for your answers.
(a) h is a twice-differentiable function of x.
(b) h and
dh dx are both continuous.
/
x .
(c) The graph of h has a horizontal tangent at
1
x .
(d) h has a local maximum at
1
x .
(e) h has a local minimum at
1
x .
(f) The graph of h has an inflection point at
1
x .
(g) The graph of
dh dx crosses the x-axis at
/
1
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