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Questions and Answers
What is the first step in finding dy/dx for the curve defined by $6x^2 + 3xy + 2y^2 + 17y = 96$?
What is the first step in finding dy/dx for the curve defined by $6x^2 + 3xy + 2y^2 + 17y = 96$?
At the point (4,0), what is the slope of the tangent line to the curve $6x^2 + 3xy + 2y^2 + 17y = 96$?
At the point (4,0), what is the slope of the tangent line to the curve $6x^2 + 3xy + 2y^2 + 17y = 96$?
What is the purpose of using the tangent line to approximate the value of k at the point (3.8, k)?
What is the purpose of using the tangent line to approximate the value of k at the point (3.8, k)?
Which of the following statements about the function g(x) = x·f(x) is true regarding the closed interval [-1, 5]?
Which of the following statements about the function g(x) = x·f(x) is true regarding the closed interval [-1, 5]?
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According to the Intermediate Value Theorem, what can be concluded about g(x) in the interval (1, 3)?
According to the Intermediate Value Theorem, what can be concluded about g(x) in the interval (1, 3)?
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What is the expression for dy/dx at the point (4,0) for the curve defined by $6x^2 + 3xy + 2y^2 + 17y = 96$?
What is the expression for dy/dx at the point (4,0) for the curve defined by $6x^2 + 3xy + 2y^2 + 17y = 96$?
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What is the equation of the tangent line to the curve at the point (4,0)?
What is the equation of the tangent line to the curve at the point (4,0)?
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Using the tangent line approximation, what is the estimated value of k for the point (3.8,k)?
Using the tangent line approximation, what is the estimated value of k for the point (3.8,k)?
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What equation can be solved to find the actual value of k such that the point (3.8,k) is on the curve?
What equation can be solved to find the actual value of k such that the point (3.8,k) is on the curve?
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What can be deduced about g(x) concerning the value -2 based on the Intermediate Value Theorem within the interval (1, 3)?
What can be deduced about g(x) concerning the value -2 based on the Intermediate Value Theorem within the interval (1, 3)?
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Study Notes
Calculus AB - Section II, Part B
- Calculator not allowed for this part
- Show all work and justify answers
Problem 1
- Curve equation: 6x² + 3xy + 2y² + 17y = 96
- Part (a): Find the derivative dy/dx
- Part (b): Find the equation of the tangent line at (4,0)
- Part (c): Use the tangent line to approximate k for point (3.8,k) on the curve.
- Part (d): Find the actual value of k so that (3.8,k) is on the curve (equation)
Problem 2
- Graph of f(x) given for the closed interval -1 ≤ x ≤ 5
- Horizontal tangents: at x = 1, x = 3
- f’(2) = -2
- Part (a): g(x) = x * f(x). Find the equation of the tangent line at x = 2 for g(x)
- Part (b): Find the average rate of change of g(x) for -1 ≤ x ≤ 5
- Part (c): Show that g(x) = -2 on the interval 1 < x ≤ 3 using the Intermediate Value Theorem
- Part (d): h(x) is the inverse of g(x). Find h’(-2)
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Description
This quiz focuses on derivatives, tangent lines, and approximation techniques using the calculus concepts taught in Calculus AB. It includes tasks of finding derivatives, tangent lines, and applying the Intermediate Value Theorem. Solve specific problems on a given curve and investigate properties of functions over a closed interval.
