In Problems 11–13, use the Fundamental Theorem of Calculus and the given graph. Each tick mark on the axes below represents one unit. F 1 f x d x 4 6.2 a n d f 1 3. F 4 g iv e n th a t f 4 7. 3 AP Calculus Review General Tips for the Exam Show all work. Always show how you set up the problem, even if you use the calculator to find the derivative or integral. An answer without an integral will not get full credit, even if it is correct. Graphs or sign charts used as justification MUST be labeled. Do not round partial answers. 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. Snow is falling at a rate of r(t) = 2e –0.1t inches per hour, where t is the time in hours since the beginning of the snowfall. Which of the following expressions gives the amount of snow, in inches, that falls from time t = 0 to time t = 5 hours? Search this site. Class Information. Weekly Timeline. Pre-Calc Review. Unit 1 - Limits and Continuity. Unit 2 - Derivatives.
Unit 1 - Limits and Continuity
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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.
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
Ap Calculus Unit 1 Review
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)
Review 1ap Calculus Definition
Substituting x=-0.9 into the equation of the tangent line yields:
5+2(-0.9+1) = 5+2(0.1) = 5.2
That’s (C).
Ap Calculus Chapter 1 Review
For more practice questions, check out our AP Calculus Prep Plus book.