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  1. AP Calculus
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Analytical Applications of Differentiation

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

If the function f(x)=x3−4xf(x) = x^3 - 4xf(x)=x3−4x has a local maximum at x=ax = ax=a, what must be true about f′(a)f'(a)f′(a)?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

What justification could there be for applying Lagrange multipliers in solving an optimization problem involving constraints rather than solely relying on finding derivatives?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

What is optimization in the context of calculus?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

Why is it important to pay attention to the wording in optimization problems?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

When using optimization techniques, what must be true about any critical points found within the domain of function g(t)g(t)g(t)?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

When optimizing a function, what does it mean to find a critical point?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

For an optimization problem concerning revenues represented by the function R(p)=−3p2+36pR(p) = -3p^2 + 36pR(p)=−3p2+36p, where p represents price per unit in dollars, how would one confirm that p=6p=6p=6 yields maximum revenue?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

If the function f(x)=13x3−kx2+12f(x) = \frac{1}{3}x^3 - kx^2 + 12f(x)=31​x3−kx2+12 has a local maximum at x=2x=2x=2, what is the value of kkk?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

Which condition would confirm that the critical point (c,f(c))(c,f(c))(c,f(c)) is indeed a local minimum for function f(x)f(x)f(x)?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

What type of optimization problem involves finding the minimum cost to construct a box with a fixed volume?