Worksheet 4.3 - The Fundamental Theorem Of Calculus Worksheet With Answers - Calculus Maximus Page 3
ADVERTISEMENT
1
2
3
4
5
6
7
8
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
x y
5
at the point 0, 5
(b) Find the average value of f x on the closed interval
1,1 .
8. Suppose f has a negative derivative for all values of x and that
f
1
0
. Which of the following
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.
/
(c) The graph of h has a horizontal tangent at
.
x
1
(d) h has a local maximum at
x
1
.
(e) h has a local minimum at
x
1
.
(f) The graph of h has an inflection point at
x
1
.
(g) The graph of
dh dx crosses the x-axis at
/
x
1
.
Page 3 of 9
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education