# Review 1ap Calculus

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. At the end of the year I suggest you review the free-response questions by type – table questions, differential equations, area/volume, rate/accumulation, graph, etc. More detailed notes on what students needed to know about each of the ten types will be the topic of future posts over the next few weeks. AB Calculus Full Overview Overview of Everything in AB Calculus N/A AB Exam Multiple Choice Practice Exam Practice Solutions AP Calculus Study Guide Study Guide for Exam AP Calculus Study Guide Final Exam Review Jeopardy Review Jeopardy Game Solutions AP Calculus AB Testing Resources Online List of Many Calc Testing Resources N/A. Learn AP®︎ Calculus AB for free—everything you need to know about limits, derivatives, and integrals to pass the AP® test. Full curriculum of exercises and videos. Ab calculus ap exam review 2 ii. Miscellaneous:.(starred problems require a calculator) (5). Given 2 particles that have respective velocities of 2 1 5 v x x and 2 x v e. Find where the 2 particles have the same accelerations on the 1. Given interval 0 5 x.

**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

## Ap Calculus Precalculus Review #1

**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:

## Ap Calculus Unit 1 Review

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

That’s (C).

## Ap Calculus Semester 1 Review With Answers

For more practice questions, check out our AP Calculus Prep Plus book.