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1997 AP Calculus BC Multiple Choice Questions 7,8,9 Solutions
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Sestion 7 asks for the equation of the tangent line to the graph of f at 3,5. Using the given information, you can find the equation of the tangent line by taking y minus the given value of 5, setting this equal to y prime at 3 which from the graph is 2, and then doing x minus the given value of x which is 3. Therefore, the equation of the tangent line is y minus 5 equals 2 times x minus 3, or y equals 2x minus 1.
In Question 8, you need to find the number of points of inflection on the graph of f. Points of inflection occur when the second derivative switches from positive to negative or negative to positive. By looking at the graph of f prime, you can see that there are six points of inflection on the original function f.
Finally, in Question 9, you need to determine the value of x where the absolute minimum of f occurs. To do this, you need to understand that the graph of f increases from zero to six, then decreases from six to eight, but the decrease from six to eight is much smaller than the increase from zero to six. Therefore, the absolute minimum occurs somewhere on the left side of the graph. Using definite integrals, you can represent the change from the lowest point to the highest point as the definite integral from 0 to 6 of f prime of x dx, and the change from 6 to 8 as the definite integral from 6 to 8 of f prime of x dx. Since the absolute minimum occurs before the change from negative to positive, the value of x where the absolute minimum occurs is between 0 and 6.
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1️⃣ What is Question 7 asking for?
Answer The equation of the tangent line to the graph of f at 3,5.
2️⃣ How can you find the equation of the tangent line in Question 7?
Answer By taking y minus the given value of 5, setting this equal to y prime at 3 which from the graph is 2, and then doing x minus the given value of x which is 3.
3️⃣ What are points of inflection?
Answer Points of inflection occur when the second derivative switches from positive to negative or negative to positive.
4️⃣ How many points of inflection are on the graph of f in Question 8?
Answer There are six points of inflection on the original function f.
5️⃣ How can you determine the value of x where the absolute minimum of f occurs in Question 9?
Answer Using definite integrals, you can represent the change from the lowest point to the highest point as the definite integral from 0 to 6 of f prime of x dx, and the change from 6 to 8 as the definite integral from 6 to 8 of f prime of x dx. The absolute minimum occurs before the change from negative to positive.
( 3,5)
8. How many points of inflection does the graph of f have?
9. At what value of x does the absolute minimum of f occur?
AP Calculus BC Practice Questions
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In Question 8, you need to find the number of points of inflection on the graph of f. Points of inflection occur when the second derivative switches from positive to negative or negative to positive. By looking at the graph of f prime, you can see that there are six points of inflection on the original function f.
Finally, in Question 9, you need to determine the value of x where the absolute minimum of f occurs. To do this, you need to understand that the graph of f increases from zero to six, then decreases from six to eight, but the decrease from six to eight is much smaller than the increase from zero to six. Therefore, the absolute minimum occurs somewhere on the left side of the graph. Using definite integrals, you can represent the change from the lowest point to the highest point as the definite integral from 0 to 6 of f prime of x dx, and the change from 6 to 8 as the definite integral from 6 to 8 of f prime of x dx. Since the absolute minimum occurs before the change from negative to positive, the value of x where the absolute minimum occurs is between 0 and 6.
Watch this video to improve your Calculus skills and ace your exams! 🎓🏆 Don't forget to like and subscribe for more math content.
1️⃣ What is Question 7 asking for?
Answer The equation of the tangent line to the graph of f at 3,5.
2️⃣ How can you find the equation of the tangent line in Question 7?
Answer By taking y minus the given value of 5, setting this equal to y prime at 3 which from the graph is 2, and then doing x minus the given value of x which is 3.
3️⃣ What are points of inflection?
Answer Points of inflection occur when the second derivative switches from positive to negative or negative to positive.
4️⃣ How many points of inflection are on the graph of f in Question 8?
Answer There are six points of inflection on the original function f.
5️⃣ How can you determine the value of x where the absolute minimum of f occurs in Question 9?
Answer Using definite integrals, you can represent the change from the lowest point to the highest point as the definite integral from 0 to 6 of f prime of x dx, and the change from 6 to 8 as the definite integral from 6 to 8 of f prime of x dx. The absolute minimum occurs before the change from negative to positive.
( 3,5)
8. How many points of inflection does the graph of f have?
9. At what value of x does the absolute minimum of f occur?
AP Calculus BC Practice Questions
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Our T-Shirt Merch:
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