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Calculus Derivatives and Functions

Calculus Derivatives and Functions

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

Mr. Tarrou explains the significance of horizontal tangent lines and how to analyze derivatives to find relative extrema. He provides examples using polynomial and trigonometric functions, demonstrating the application of the quadratic formula and trigonometric identities to solve for points where the derivative equals zero.

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9 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it important to know where the tangent lines of a function are horizontal?

To calculate the function's range

To analyze relative extrema

To find points of inflection

To determine the function's domain

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does it indicate if the first derivative is negative to the left and positive to the right of a point?

A relative minimum

A constant function

A relative maximum

A point of inflection

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What can be concluded if the derivative is zero but there is no sign change?

A relative maximum

A relative minimum

A point of inflection

Not a relative extremum

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the function f(x) = x^3 - 4x^2 + x + 6?

3x^2 - 4x + 1

x^2 - 8x + 6

3x^2 - 8x + 1

3x^3 - 8x^2 + 1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the quadratic formula used in the example?

The polynomial is linear

The polynomial is not factorable

The polynomial is a perfect square

The polynomial is already solved

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of the solution for x in the polynomial example?

4 ± √13 / 3

8 ± √52 / 6

2 ± √13 / 3

6 ± √13 / 4

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of f(x) = 2sin(x) + cos(2x)?

2cos(x) + 2sin(2x)

cos(x) - 2sin(2x)

2sin(x) + cos(2x)

2cos(x) - sin(2x)

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