Learn to find the tangent line through the point of the function

The video tutorial explains how to find the tangent line to a curve at a given point, even if the point is not on the graph. It covers the use of derivatives to determine the slope of the tangent line and the process of solving for the equation of the tangent line. The tutorial also includes a graphical interpretation of the problem, showing how to find the X and Y values where the tangent line intersects the curve. Finally, it demonstrates how to calculate the slopes for the tangent lines at specific points.

What is the main difference between the current problem and the previous one discussed?

• The current problem requires finding a tangent line at a specific point on the graph.

• The current problem does not involve any tangent lines.

• The current problem involves finding a tangent line through a point not on the graph.

• The previous problem involved finding a tangent line through a point not on the graph.

What is the derivative of the function y = X^3 - 9X?

• 3X^2 + 9

• 3X^2 - 9

• 9X^2 - 3

• X^3 - 9

Why is it necessary to set the tangent line equation equal to the function?

• To determine the Y-intercept of the tangent line.

• To find the X values where the tangent line intersects the function.

• To verify if the point is on the graph.

• To find the slope of the tangent line.

What are the X values where the tangent lines intersect the function?

• 1/2 and 2

• 0 and 3/2

• 1 and 2

• 0 and 3

How is the Y value calculated for a given X value?

• By substituting the X value into the derivative.

• By substituting the X value into the original function.

• By setting the X value equal to zero.

• By using the slope-intercept form of the line.

What is the slope of the tangent line at X = 0?

• -9

• 0

• 9

• 3

What is the equation of the tangent line at the point (3/2, -81/8)?

• y + 81/8 = -9/4(x - 3/2)

• y - 9 = 9/4(x - 1)

• y + 9 = -9/4(x - 1)

• y - 81/8 = 9/4(x - 3/2)