Analyzing Increasing Functions

The video tutorial introduces the concepts of increasing and decreasing functions, explaining how they relate to differentiation. It covers the characteristics of these functions, including monotone increasing and decreasing functions. A theorem is presented to determine if a function is increasing or decreasing at a point. The video concludes with examples and exercises to find intervals where functions increase or decrease.

What is the primary mathematical tool used to analyze increasing and decreasing functions?

• Differentiation

• Integration

• Geometry

• Algebra

How can you visually identify an increasing function on a graph?

• The graph forms a circle

• The graph moves upward

• The graph remains constant

• The graph moves downward

What is a monotone increasing function?

• A function that increases and decreases

• A function that neither increases nor decreases

• A function that only increases

• A function that only decreases

According to the theorem, when is a function increasing at a point?

• When its first derivative is zero

• When its second derivative is zero

• When its second derivative is positive

• When its first derivative is positive

In Example 1, what inequality is solved to find the increasing interval?

• 2x + 5 < 0

• 2x + 5 > 0

• 2x - 5 > 0

• 2x - 5 < 0

In Example 2, what is the nature of the function analyzed?

• Linear

• Exponential

• Cubic

• Quadratic

What is the derivative of the function in Example 3?

• x/4 + 8

• x/2 + 8

• x/4 - 8

• x/2 - 8