Determine the derivative expanding a binomial to use the power rule

The video tutorial explains how to find the tangent line to a given function and determine the instantaneous rate of change, or slope, of that tangent line. It begins with an introduction to the problem, followed by steps to find the derivative using the power rule. The tutorial includes a correction of a calculation error and demonstrates the application of the power rule to find the derivative. Finally, it shows how to calculate the slope of the tangent line at a specific point.

What is the primary goal when finding a tangent line to a function?

• To identify the function's roots

• To calculate the area under the curve

• To find the slope of the tangent line

• To determine the function's maximum value

Which mathematical rule is applied to find the derivative of the function in the video?

• Quotient Rule

• Power Rule

• Product Rule

• Chain Rule

What is the corrected expression for the function after rewriting it?

• 2x + 1 times 2x + 1

• 4x squared plus 4x

• x squared plus 2x plus 1

• 3x squared plus 2x

How is the slope of the tangent line at a specific point determined?

• By solving the function for y

• By plugging the x-coordinate into the derivative

• By integrating the function

• By finding the second derivative

What is the slope of the function at the point (0,1) as calculated in the video?

• 2

• 8

• 4

• 6