Understanding the Alternate Form of the Derivative

What is the alternate form of the derivative primarily used to find?

• The x-intercept of a function

• The maximum value of a function

• The slope of a tangent line

• The area under a curve

In the context of derivatives, what does the numerator of the slope formula represent?

• The change in horizontal values

• The change in the function's value

• The total area under the curve

• The x-coordinate of the tangent point

What happens to the secant line as x approaches a?

• It diverges from the tangent line

• It becomes a horizontal line

• It better approximates the tangent line

• It becomes a vertical line

What is the purpose of taking the limit as x approaches a in the derivative definition?

• To find the maximum value of the function

• To determine the slope of the tangent line

• To calculate the area under the curve

• To identify the x-intercept

What is the value of 'a' when finding the slope of the tangent line at a specific point in this example?

• 125

• 10

• 5

• 3