Tangent and Normal Lines Concepts

The video tutorial explains how to find the equations of the tangent and normal lines to a function at a specific point. It begins by introducing the concepts of tangent and normal lines, then derives the equation of the tangent line using the derivative of the function. The tutorial continues by finding the equation of the normal line, which involves calculating the negative reciprocal of the tangent line's slope. Finally, the video verifies the results graphically, ensuring the tangent line is tangent to the curve and the normal line is perpendicular at the given point.

What is the relationship between the tangent line and the curve at a given point?

• The tangent line is a quadratic approximation of the curve.

• The tangent line is parallel to the curve.

• The tangent line is a linear approximation of the curve at that point.

• The tangent line is perpendicular to the curve.

Which formula is used to find the equation of the tangent line?

• y = ax^2 + bx + c

• y = x^3 + 5x + 2

• y = mx + b

• y - y1 = m(x - x1)

What is the derivative of the function x^3 - 5x + 2?

• 3x^2 + 5

• 3x^2 - 5

• x^2 - 5

• 3x^2 - 5x

What is the slope of the tangent line at x = -1?

• 2

• -2

• 1

• -1

What is the equation of the tangent line at the point (-1, 6)?

• y = 2x + 6

• y = -2x + 6

• y = 2x + 4

• y = -2x + 4

How is the slope of the normal line related to the slope of the tangent line?

• It is the negative reciprocal of the slope of the tangent line.

• It is half the slope of the tangent line.

• It is twice the slope of the tangent line.

• It is the same as the slope of the tangent line.

What is the slope of the normal line if the slope of the tangent line is -2?

• -1/2

• 1/2

• 2

• -2

What is the equation of the normal line at the point (-1, 6)?

• y = 1/2x + 6

• y = -1/2x + 6

• y = -1/2x + 13/2

• y = 1/2x + 13/2

What is the purpose of graphically verifying the tangent and normal lines?

• To ensure the lines intersect at the correct point.

• To verify the lines are tangent to the curve.

• To check if the lines are parallel.

• To confirm the lines are perpendicular at the point of tangency.

What is the y-intercept of the normal line equation y = 1/2x + 13/2?

• 1/2

• 4

• 6

• 13/2