Understanding Tangent Lines and Inverse Functions

The video tutorial explains how to find the slope of the tangent line to the inverse of a given function at a specific point. It starts by establishing the relationship between the function and its inverse, then uses the chain rule to calculate the derivative of the original function. The slope of the tangent line to the inverse function is found by taking the reciprocal of the derivative at the corresponding point. Finally, the equation of the tangent line is derived using point-slope form, and the solution is verified graphically.

What is the relationship between a function and its inverse at a given point?

• They are parallel.

• They intersect at the origin.

• Their slopes are reciprocals.

• They have the same slope.

If F of 1 equals 3, what point lies on the graph of the inverse function?

• (3, 1)

• (3, 3)

• (1, 1)

• (1, 3)

How do you find the slope of the tangent line to the inverse function at a point?

• By using the reciprocal of the derivative of the original function at the corresponding point.

• By using the midpoint formula.

• By calculating the second derivative of the original function.

• By finding the derivative of the inverse function directly.

What rule is applied to find the derivative of the given function?

• Power Rule

• Chain Rule

• Quotient Rule

• Product Rule

What is the derivative of the function F(x) = 6 / (1 + x^2)?

• -6x / (1 + x^2)

• -12x / (1 + x^2)^2

• 6x / (1 + x^2)

• 12x / (1 + x^2)^2

What is the slope of the tangent line to the inverse function at the point (3, 1)?

• -1/3

• 1

• -1

• 1/3

What is the equation of the tangent line to the inverse function at the point (3, 1)?

• y = 1/3x - 2

• y = -1/3x + 2

• y = -1/3x - 2

• y = 1/3x + 2

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

• Vertex form

• Slope-intercept form

• Point-slope form

• Standard form

What color represents the inverse function in the graph?

• Blue

• Red

• Green

• Orange

What is the final conclusion about the tangent line's equation?

• It is incorrect.

• It is verified graphically.

• It needs further simplification.

• It is only an approximation.