AP Calculus AB Review Week 2 Derivatives and Tangents Advanced Placement AAP Review will be held in room 315 and 312on Tuesdays and Thursdays. The week of March 23rd we will be reviewing Derivatives and Tangents. The session will begin in room 315 with a brief review of the weekly topic. AP Calculus AB eLearning Guide- Week 2 April 20 - 24, 2020 O b j e c ti v e s Function Analysis, FTC, Average Rate of Change, Absolute Extrema, L'Hospital's Rule, Evaluating Limits, Slope Fields, Differential Equations, Linear Approximation, Equation of. AP Calculus AB Exam Information. You can expect to take this AP exam upon completion of your AP Calculus AB course in high school. If you earn a high score on the exam, you can become eligible for. AP Calculus AB Exam and AP Calculus BC Exam, and they serve as examples of the types of questions that appear on the exam. Each question is accompanied by a table containing the main learning objective(s), essential knowledge statement(s), and Mathematical Practices for AP Calculus that the question addresses.
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Test your readiness for the AP Calculus exam with this quiz!
Answer 1
A: If the graph of a function has a sharp point, the function is not differentiable at that point. This is because the slopes directly to the left and right of the point do not approach the same value.
An absolute value function has a sharp point at its vertex. The graph off(x)=|x + 4| is a horizontal translation (to the left 4 units) of the standard absolute value function, y =|x|, which has vertex (0, 0). Thus, the vertex of fis (-4, 0), which means the function is not differentiable at x =-4. Choice (A) is correct.
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D: The only discontinuities that are removable are holes and holes with a point above or below—this function has neither. The function has 2 jump discontinuities (gaps), at x=-2 and x= 0, but neither of these is removable.
Answer 3
D: Examine the values in the table: f(x) increases as x gets larger, which indicates that f′(x), the slope of the function, is positive. This means f′(x)> 0, so eliminate (A) and (B).
To choose between (C) and (D), take a closer look at the slopes. The slope between the first pair of points is 3, and the slope between the second pair of points is also 3, so f′(x) is constant. This means f′′(x), which is the derivative of f′(x), must be 0. Choice (D) is correct
Answer 4
C: To use a local linear approximation, you need to find the equation of the tangent line. You've been given all the information you need in the question stem; you just need to piece it all together. The point on the function is given by f(-1)= 5, which translates to the point (-1, 5). The slope of the tangent line at x=-1 is given by f'(-1)= 2, so the slope is 2. Now the point-slope form of the tangent line is:
Hey another unblocked game site play. Answer 2
D: The only discontinuities that are removable are holes and holes with a point above or below—this function has neither. The function has 2 jump discontinuities (gaps), at x=-2 and x= 0, but neither of these is removable.
Answer 3
D: Examine the values in the table: f(x) increases as x gets larger, which indicates that f′(x), the slope of the function, is positive. This means f′(x)> 0, so eliminate (A) and (B).
To choose between (C) and (D), take a closer look at the slopes. The slope between the first pair of points is 3, and the slope between the second pair of points is also 3, so f′(x) is constant. This means f′′(x), which is the derivative of f′(x), must be 0. Choice (D) is correct
Answer 4
C: To use a local linear approximation, you need to find the equation of the tangent line. You've been given all the information you need in the question stem; you just need to piece it all together. The point on the function is given by f(-1)= 5, which translates to the point (-1, 5). The slope of the tangent line at x=-1 is given by f'(-1)= 2, so the slope is 2. Now the point-slope form of the tangent line is:
y-5 = 2(x-(-1))
y = 5+2(x+1)
Substituting x=-0.9 into the equation of the tangent line yields:
5+2(-0.9+1) = 5+2(0.1) = 5.2
Week 2ap Calculus Class
That's (C).
Week 2 Ap Calculus College Board
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