If w ( x ) = f ( x ) q ( x ) w\left(x\right)=f\left(x\right)q\left(x\right) w ( x ) = f ( x ) q ( x ) , then w ′ ( x ) = w'\left(x\right)= w ′ ( x ) =

f ′ ( x ) q ( x ) + f ( x ) q ′ ( x ) f'\left(x\right)q\left(x\right)+f\left(x\right)q'\left(x\right) f ′ ( x ) q ( x ) + f ( x ) q ′ ( x )

f ′ ( x ) q ′ ( x ) f'\left(x\right)q'\left(x\right) f ′ ( x ) q ′ ( x )

f ′ ( x ) q ′ ( x ) + f ( x ) q ( x ) f'\left(x\right)q'\left(x\right)+f\left(x\right)q\left(x\right) f ′ ( x ) q ′ ( x ) + f ( x ) q ( x )

f ′ ( q ( x ) ) q ′ ( x ) f'\left(q\left(x\right)\right)q'\left(x\right) f ′ ( q ( x ) ) q ′ ( x )

Evaluate lim ⁡ x → π 4 cos ⁡ x − cos ⁡ ( π 4 ) x − π 4 \lim_{x\rightarrow\frac{\pi}{4}}\frac{\cos x-\cos\left(\frac{\pi}{4}\right)}{x-\frac{\pi}{4}} x → 4 π lim x − 4 π cos x − cos ( 4 π )

− 2 2 -\frac{\sqrt{2}}{2} − 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 2 \frac{\sqrt{2}}{2} 2 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

For a particle moving along the x-axis, the particle's speed equals 2 when

∣ v ( t ) ∣ = 2 \left|v\left(t\right)\right|=2 ∣ v ( t ) ∣ = 2

v ( t ) = 2 v\left(t\right)=2 v ( t ) = 2

a ( t ) = 2 a\left(t\right)=2 a ( t ) = 2

∣ a ( t ) ∣ = 2 \left|a\left(t\right)\right|=2 ∣ a ( t ) ∣ = 2

If f ( x ) = ∫ 4 x ( cos ⁡ ( 2 t ) + 3 ) d t f\left(x\right)=\int_4^x\left(\cos\left(2t\right)+3\right)dt f ( x ) = ∫ 4 x ( cos ( 2 t ) + 3 ) d t , then f ′ ( x ) = f'\left(x\right)= f ′ ( x ) =

cos ⁡ ( 2 x ) + 3 \cos\left(2x\right)+3 cos ( 2 x ) + 3

1 2 sin ⁡ ( 2 x ) + 3 x \frac{1}{2}\sin\left(2x\right)+3x 2 1 sin ( 2 x ) + 3 x

cos ⁡ ( 2 x ) \cos\left(2x\right) cos ( 2 x )

2 cos ⁡ ( 2 x ) + 3 2\cos\left(2x\right)+3 2 cos ( 2 x ) + 3

What are the conditions that satisfy the mean value theorem, and what does it mean?

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval ( a , b ) (that is a < c < b ) such that f'(c)=(f(b)- f(a))/ (b-a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval ( a , b ) (that is a < c < b ) such that

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval ( a , b ) (that is a < c < b ) such that f'(c)=(f(b)- f(a))/ (b-a)

Continuous on the open and differentiable on the open, and then there is no number c in the interval ( a , b ) (that is a < c < b ) such that f'(c)=(f(b)- f(a))/ (b-a)

AP Calculus Final First 15 :)

Authored by Tanya Hickson

Mathematics

12th Grade

CCSS covered

Used 3+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

36 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the limit?

Infinity

DNE

Find the second derivative of the function:
f (x) = 2x - 5x⁶

f ''(x)= 2 - 30x

f ''(x) = 2-30x⁵

f ''(x) = -30x⁵

f ''(x) = -150x⁴

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Intermediate Value Theorem

Rolle's Theorem

Average Rate of Change

Average Value of f

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Average Rate of Change

Average Value of f

Intermediate Value Theorem

Rolle's Theorem

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

38 questions

FA-5.4-5.6: Investing Review

Quiz

•

9th - 12th Grade

34 questions

zadania maturalne

Quiz

•

10th - 12th Grade

31 questions

Polygon Sum Theorem, Exterior Angle Theorem and Triangles

Quiz

•

9th - 12th Grade

41 questions

Venn Diagrams I

Quiz

•

9th - 12th Grade

31 questions

Algebra #1

Quiz

•

10th - 12th Grade

40 questions

MATEMATIKA 8 SMT 1

Quiz

•

8th Grade - University

33 questions

M3 Fall Final Review

Quiz

•

9th - 12th Grade

40 questions

PENILAIAN AKHIR SEKOLAH TP 2024/2025

Quiz

•

12th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

29 questions

Alg. 1 Section 5.1 Coordinate Plane

Quiz

•

9th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

11 questions

FOREST Effective communication

Lesson

•

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

Discover more resources for Mathematics

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

14 questions

Making Inferences From Samples

Quiz

•

7th - 12th Grade

23 questions

CCG - CH8 Polygon angles and area Review

Quiz

•

9th - 12th Grade

20 questions

Domain and Range Spiral Review

Quiz

•

9th - 12th Grade

10 questions

Dividing a polynomial by a monomial

Quiz

•

10th - 12th Grade

16 questions

Explore Triangle Congruence Theorems

Quiz

•

9th - 12th Grade

17 questions

Interpreting Graphs Of Functions

Quiz

•

8th - 12th Grade

15 questions

Explore Exponential Functions and Their Applications

Quiz

•

9th - 12th Grade

AP Calculus Final First 15 :)

What is the limit?

Find the second derivative of the function:f (x) = 2x - 5x6

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 the second derivative of the function:
f (x) = 2x - 5x⁶