| C:/Users/Aisha/Downloads/6083.%20Calculus_%2011th%20Edition_%20Howard%20Anton%20 %20lrl%20C.%20Bivens%20_%20Stephen%20Davis. -1 -2 1 -3 -4 0 1 2 3 4 5678 9 10 -5 Figure Ex-4 -6 5. Find a function f such that the graph of f contains the point (1,5) and such that for every value of to the graph of f at xo is parallel to the tangent line to the graph of y = x at xo. -7 -5-4-3-2-1 01 2 3 4 5 1Figure Ex-2 the tangent line 3. Let f(x) = x2 x. (a) Find a point b such that the slope of the secant line through (0,0) and (b, f(b)) is 1. %3D EXERCISE SET 3.8 Graphing Utility 1-4 Verify that the hypotheses of Rolle's Theorem are satisfied on the given interval, and find all values of c in that interval that satisfy the conclusion of the theorem. 2. f(x) = }x – Vx; [0, 4] 3. f(x) = cos x; [T/2,37/2] 4. f(x) = (x² – 1)/(x- 2): [- 1, 1] %3D %3D 1. f(x) = x² - 8x + 15; [3,5] 196 Chapter 3 / The Derivative in Graphing and Applications 5-8 Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and find all values of c in that interval that satisfy the conclusion of the theorem. (b) Explain why the result in part (a) does not contra- dict the Mean-Value Theorem. 17. (a) Show that if f is differentiable on (-00,+o0), and if y = f(x) and y =f'(x) are graphed in the same co- ordinate system, then between any two x-intercepts of f there is at least one x-intercept of f'. (b) Give some examples that illustrate this. 5. f(x) = x² - x; [-3, 5] %3D =x' +x-4; [-1,2] 7. f(x) = 25- x²; [-5,3] %3D 8. f(x) = x-; [3,4] 18. Review Formulas (6) and (7) in Section 2.1 and use the Mean-Value Theorem to show that if f is differentiable on (-00, +o0), then for any interval [xo,x] there is at least one point in (xo, x1) where the instantaneous rate 9. (a) Find an interval [a, b] on which f(x) = x* +x - x² +x- 2 %3D satisfies the hypotheses of Rolle's Theorem. 3210
| C:/Users/Aisha/Downloads/6083.%20Calculus_%2011th%20Edition_%20Howard%20Anton%20 %20lrl%20C.%20Bivens%20_%20Stephen%20Davis. -1 -2 1 -3 -4 0 1 2 3 4 5678 9 10 -5 Figure Ex-4 -6 5. Find a function f such that the graph of f contains the point (1,5) and such that for every value of to the graph of f at xo is parallel to the tangent line to the graph of y = x at xo. -7 -5-4-3-2-1 01 2 3 4 5 1Figure Ex-2 the tangent line 3. Let f(x) = x2 x. (a) Find a point b such that the slope of the secant line through (0,0) and (b, f(b)) is 1. %3D EXERCISE SET 3.8 Graphing Utility 1-4 Verify that the hypotheses of Rolle's Theorem are satisfied on the given interval, and find all values of c in that interval that satisfy the conclusion of the theorem. 2. f(x) = }x – Vx; [0, 4] 3. f(x) = cos x; [T/2,37/2] 4. f(x) = (x² – 1)/(x- 2): [- 1, 1] %3D %3D 1. f(x) = x² - 8x + 15; [3,5] 196 Chapter 3 / The Derivative in Graphing and Applications 5-8 Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and find all values of c in that interval that satisfy the conclusion of the theorem. (b) Explain why the result in part (a) does not contra- dict the Mean-Value Theorem. 17. (a) Show that if f is differentiable on (-00,+o0), and if y = f(x) and y =f'(x) are graphed in the same co- ordinate system, then between any two x-intercepts of f there is at least one x-intercept of f'. (b) Give some examples that illustrate this. 5. f(x) = x² - x; [-3, 5] %3D =x' +x-4; [-1,2] 7. f(x) = 25- x²; [-5,3] %3D 8. f(x) = x-; [3,4] 18. Review Formulas (6) and (7) in Section 2.1 and use the Mean-Value Theorem to show that if f is differentiable on (-00, +o0), then for any interval [xo,x] there is at least one point in (xo, x1) where the instantaneous rate 9. (a) Find an interval [a, b] on which f(x) = x* +x - x² +x- 2 %3D satisfies the hypotheses of Rolle's Theorem. 3210
Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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![| C:/Users/Aisha/Downloads/6083.%20Calculus_%2011th%20Edition_%20Howard%20Anton%20 %20lrl%20C.%20Bivens%20_%20Stephen%20Davis.
-1
-2
1
-3
-4
0 1 2 3 4 5678 9 10
-5
Figure Ex-4
-6
5. Find a function f such that the graph of f contains the point
(1,5) and such that for every value of
to the graph of f at xo is parallel to the tangent line to the
graph of y = x at xo.
-7
-5-4-3-2-1 01 2 3 4 5
1Figure Ex-2
the tangent line
3. Let f(x) = x2 x.
(a) Find a point b such that the slope of the secant line
through (0,0) and (b, f(b)) is 1.
%3D
EXERCISE SET 3.8
Graphing Utility
1-4 Verify that the hypotheses of Rolle's Theorem are satisfied
on the given interval, and find all values of c in that interval that
satisfy the conclusion of the theorem.
2. f(x) = }x – Vx; [0, 4]
3. f(x) = cos x; [T/2,37/2]
4. f(x) = (x² – 1)/(x- 2): [- 1, 1]
%3D
%3D
1. f(x) = x² - 8x + 15; [3,5]
196 Chapter 3 / The Derivative in Graphing and Applications
5-8 Verify that the hypotheses of the Mean-Value Theorem are
satisfied on the given interval, and find all values of c in that
interval that satisfy the conclusion of the theorem.
(b) Explain why the result in part (a) does not contra-
dict the Mean-Value Theorem.
17. (a) Show that if f is differentiable on (-00,+o0), and if
y = f(x) and y =f'(x) are graphed in the same co-
ordinate system, then between any two x-intercepts
of f there is at least one x-intercept of f'.
(b) Give some examples that illustrate this.
5. f(x) = x² - x; [-3, 5]
%3D
=x' +x-4; [-1,2]
7. f(x) = 25- x²; [-5,3]
%3D
8. f(x) = x-; [3,4]
18. Review Formulas (6) and (7) in Section 2.1 and use the
Mean-Value Theorem to show that if f is differentiable
on (-00, +o0), then for any interval [xo,x] there is at
least one point in (xo, x1) where the instantaneous rate
9. (a) Find an interval [a, b] on which
f(x) = x* +x - x² +x- 2
%3D
satisfies the hypotheses of Rolle's Theorem.
3210](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd754338b-a440-43cc-93d8-3b0ee7fbda70%2F05faff43-a352-4f9c-b5e2-eeac246ffb82%2Fxsrnlx.jpeg&w=3840&q=75)
Transcribed Image Text:| C:/Users/Aisha/Downloads/6083.%20Calculus_%2011th%20Edition_%20Howard%20Anton%20 %20lrl%20C.%20Bivens%20_%20Stephen%20Davis.
-1
-2
1
-3
-4
0 1 2 3 4 5678 9 10
-5
Figure Ex-4
-6
5. Find a function f such that the graph of f contains the point
(1,5) and such that for every value of
to the graph of f at xo is parallel to the tangent line to the
graph of y = x at xo.
-7
-5-4-3-2-1 01 2 3 4 5
1Figure Ex-2
the tangent line
3. Let f(x) = x2 x.
(a) Find a point b such that the slope of the secant line
through (0,0) and (b, f(b)) is 1.
%3D
EXERCISE SET 3.8
Graphing Utility
1-4 Verify that the hypotheses of Rolle's Theorem are satisfied
on the given interval, and find all values of c in that interval that
satisfy the conclusion of the theorem.
2. f(x) = }x – Vx; [0, 4]
3. f(x) = cos x; [T/2,37/2]
4. f(x) = (x² – 1)/(x- 2): [- 1, 1]
%3D
%3D
1. f(x) = x² - 8x + 15; [3,5]
196 Chapter 3 / The Derivative in Graphing and Applications
5-8 Verify that the hypotheses of the Mean-Value Theorem are
satisfied on the given interval, and find all values of c in that
interval that satisfy the conclusion of the theorem.
(b) Explain why the result in part (a) does not contra-
dict the Mean-Value Theorem.
17. (a) Show that if f is differentiable on (-00,+o0), and if
y = f(x) and y =f'(x) are graphed in the same co-
ordinate system, then between any two x-intercepts
of f there is at least one x-intercept of f'.
(b) Give some examples that illustrate this.
5. f(x) = x² - x; [-3, 5]
%3D
=x' +x-4; [-1,2]
7. f(x) = 25- x²; [-5,3]
%3D
8. f(x) = x-; [3,4]
18. Review Formulas (6) and (7) in Section 2.1 and use the
Mean-Value Theorem to show that if f is differentiable
on (-00, +o0), then for any interval [xo,x] there is at
least one point in (xo, x1) where the instantaneous rate
9. (a) Find an interval [a, b] on which
f(x) = x* +x - x² +x- 2
%3D
satisfies the hypotheses of Rolle's Theorem.
3210
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