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Differentiation and Tangent Line Concepts

Differentiation and Tangent Line Concepts

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.TF.B.7, 8.EE.B.5

Standards-aligned

Created by

Ethan Morris

FREE Resource

Standards-aligned

CCSS.HSF.TF.B.7
,
CCSS.8.EE.B.5
The video tutorial explains how to determine dy/dx using implicit differentiation for the equation x*cos(y) = 1. It covers applying the product and chain rules, solving for dy/dx, and calculating the slope of the tangent line at a specific point. The tutorial concludes with a graphical representation of the function and tangent line to illustrate the slope visually.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main goal of the problem discussed in the video?

To calculate the area under a curve

To find the value of x

To determine dy/dx and the slope of the tangent line

To solve a quadratic equation

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of equation is x * cosine y = 1?

Quadratic equation

Explicit equation

Implicit equation

Linear equation

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which rule is applied to differentiate x * cosine y?

Product rule

Power rule

Quotient rule

Chain rule

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of cosine y with respect to x?

sin y

cos y

sin y * dy/dx

cos y * dy/dx

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you solve for dy/dx after differentiating the equation?

By adding terms

By multiplying both sides by x

By dividing by x sin y

By subtracting terms

Tags

CCSS.HSF.TF.B.7

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What values are substituted into the derivative to find the slope of the tangent line?

x = 0 and y = 0

x = -2 and y = 2 pi/3

x = 1 and y = pi

x = 2 and y = pi/2

Tags

CCSS.HSF.TF.B.7

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the reference angle for 2 pi/3 in the second quadrant?

30°

45°

60°

90°

Tags

CCSS.HSF.TF.B.7

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