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Understanding Derivatives and Relative Maximums

Understanding Derivatives and Relative Maximums

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Jackson Turner

FREE Resource

The video tutorial explains the graph of f prime, the derivative of a twice differentiable function f, on a closed interval from -3 to 4. It highlights the horizontal tangents at specific x-values and discusses the areas of regions bounded by the x-axis and f prime. The tutorial then focuses on finding the x-coordinates where f has a relative maximum by analyzing the transition of f prime from positive to negative. It concludes by identifying the specific x-value where this transition occurs, indicating a relative maximum for f.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the graph of f' represent in relation to the function f?

The derivative of f

The integral of f

The second derivative of f

The original function f

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is indicated by a horizontal tangent on the graph of f'?

A point where f' is zero

A point where f is decreasing

A point where f' is undefined

A point where f is increasing

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

For a function f to have a relative maximum, what must occur with its derivative f'?

f' must transition from positive to negative

f' must be constant

f' must transition from negative to positive

f' must be zero

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a positive value of f' indicate about the function f?

f has a relative minimum

f is decreasing

f is constant

f is increasing

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a negative value of f' indicate about the function f?

f is decreasing

f is increasing

f has a relative maximum

f is constant

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

At which x-coordinate does the function f have a relative maximum?

x = 4

x = 2

x = 0

x = -3

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of the point where f' transitions from positive to negative?

It indicates a relative minimum of f

It indicates a relative maximum of f

It indicates a point of inflection

It indicates a constant value of f

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