If a function has a derivative that is negative, what does that tell you?

The concavity of the function is up

The concavity of the function is down

Is the above function differentiable at x = 0? Why?

No. The derivative would not exist at x = 0 since there is a vertical tangent.

Yes. The derivative would be equal to zero since there is a vertical tangent.

No. The derivative does not exist since <span class="katex-mathml" style="border-bottom-color: currentColor; border-bottom-style: none; border-bottom-width: 0px; border-image-outset: 0; border-image-repeat: stretch; border-image-slice: 100%; border-image-source: none; border-image-width: 1; border-left-color: currentColor; border-left-style: none; border-left-width: 0px; border-right-color: currentColor; border-right-style: none; border-right-width: 0px; border-top-color: currentColor; border-top-style: none; border-top-width: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; -ms-high-contrast-adjust: none; overflow: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; width: 1px;"> lim ⁡ x → 0 x 1 3 \lim_{x\rightarrow0}\ x^{\frac{1}{3}} x → 0 lim x 3 1 does not exist.

Yes since lim ⁡ h → 0 ( x + h ) 1 3 − x 1 3 h \lim_{h\rightarrow0}\ \frac{\left(x+h\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{h} h → 0 lim h ( x + h ) 3 1 − x 3 1 exists.

When applying calculus, the second derivative of position helps find...

acceleration of an object at any given time

the distance traveled by an object.

The velocity of a particle at any given point

All of the follow are TRUE about Ms Kwong except... Todos los siguientes son VERDADEROS sobre la Sra. Kwong, excepto ...

She is in her late 20s (> 25 years old). Ella tiene alrededor de 20 años (> 25 años).

She loves grocery shopping. A ella le encanta ir de compras.

She only wants to use an Android phone. Ella solo quiere usar un teléfono Android.

She loves to sing and acted in a school play in high school. Le encanta cantar y actuó en una obra de teatro en la escuela secundaria.

I'd love your feedback! Based on the past 3 weeks, which of the following did you like learning from the most? Please select all that apply.

Office hours / video live discussion

Emails / gchats / private comments from teacher on your work

May is Asian American Pacific Islander Heritage Month! This person was the first woman to serve as the district attorney of the state of California. Her mother is from India.

Representative Alexandria Ocasio-Cortez

Why was May selected to celebrate Asian American Pacific Islander Heritage Month? Pick 2 only.

The transcontinental railroad (which was mostly built by Chinese Americans) was completed on May 10, 1869.

The immigration of the first Japanese to the United States was on May 7, 1843.

Japanese Americans were forced to leave their homes and live in internment camps in May 1942.

The Vietnam - American war ended in May 1975.

Which of the following cases would lead to an object slowing down?

positive acceleration, negative velocity

negative acceleration, positive velocity

positive acceleration, positive velocity

negative acceleration, negative velocity

Given the sign chart for f '(x), f(x) has ...

local maxima at x = -2 and x = 4.

Given the sign chart for f '(x), f(x) has ...

a local maximum at x = -2 and a local minimum at x = 4.

a local minimum at x = -2 and a local maximum at x = 4.

Given the graph of f '(x), f(x) has ...

a local min at x = 2 and a local max at x = -6

local mins at x = -2, 5 and a local max at x = 3

AP Calculus Review - Limits, Derivatives, and Integrals

Authored by J Kwong

Mathematics

11th Grade - University

CCSS covered

Used 26+ times

AP Calculus Review - Limits, Derivatives, and Integrals

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62 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Evaluate the limit

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Evaluate the limit

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the equation of the line tangent to the function at the given point

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of csc(x)?

csc(x)cot(x)

-csc(x)cot(x)

-csc²(x)

-cot²(x)

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find h'(3)

-2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

When we "take the derivative" of a function what are we finding?

What's a derivative?

The rate at which our struggles in Calculus are increasing.

The slope of the secant line

The slope of the tangent line

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

6 -x

3x² +3y²

−x²/y²

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AP Calculus Review - Limits, Derivatives, and Integrals

Evaluate the limit

Evaluate the limit

Find the equation of the line tangent to the function at the given point

What is the derivative of csc(x)?

Find h'(3)

When we "take the derivative" of a function what are we finding?

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

Find the value for that makes f(x) continuous.

Find the average rate of change of Pete's height from 3 years old to 5 years old.

If a function has a derivative that is negative, what does that tell you?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

AP Calculus Review - Limits, Derivatives, and Integrals

Evaluate the limit

Evaluate the limit

Find the equation of the line tangent to the function at the given point

What is the derivative of csc(x)?

Find h'(3)

When we "take the derivative" of a function what are we finding?

Find dy/dx by Implicit Differentiation x3 +y3 = 36

Find the value for that makes f(x) continuous.

Find the average rate of change of Pete's height from 3 years old to 5 years old.

If a function has a derivative that is negative, what does that tell you?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find dy/dx by Implicit Differentiation
x³ +y³ = 36