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Calculus Concepts and Applications

Calculus Concepts and Applications

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
8.EE.C.7B, HSF.TF.A.2

Standards-aligned

Created by

Mia Campbell

FREE Resource

Standards-aligned

CCSS.8.EE.C.7B
,
CCSS.HSF.TF.A.2
The video tutorial explains how to find the equation of a tangent line to a cubic function at a specific point and how to calculate the area of a region bounded by two functions using integrals. It begins with defining the region R in the first quadrant, enclosed by the graphs of f(x) = 8x^3 and g(x) = sin(pi x). The tutorial then derives the equation of the tangent line to f(x) at x = 1/2 by calculating the derivative and using the point-slope form. Finally, it demonstrates how to find the area of region R by integrating the difference between the two functions from 0 to 1/2.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function f(x) as defined in the problem?

f(x) = 8x^2

f(x) = 8x^3

f(x) = sin(pi x)

f(x) = cos(pi x)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the slope of the tangent line to f(x) at x = 1/2?

3

6

12

24

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the y-intercept of the tangent line to f(x) at x = 1/2?

0

-2

2

1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which function is on top when calculating the area of region R?

h(x) = cos(pi x)

g(x) = sin(pi x)

f(x) = 8x^3

j(x) = 8x^2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the integral setup to find the area of region R?

Integral from 0 to 1 of f(x) dx

Integral from 0 to 1/2 of (g(x) - f(x)) dx

Integral from 0 to 1/2 of g(x) dx

Integral from 0 to 1 of (f(x) - g(x)) dx

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the antiderivative of sin(pi x)?

pi cos(pi x)

-cos(pi x)

1/pi sin(pi x)

-1/pi cos(pi x)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the antiderivative of -8x^3?

-16x^4

-8x^4

-2x^4

-4x^4

Tags

CCSS.HSF.TF.A.2

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