Understanding Functions and Their Inverses

The video tutorial covers evaluating a function at a specific point, calculating its derivative, finding the inverse function, and determining the derivative of the inverse function. It begins with evaluating F(2) for a given function, then moves on to finding the derivative DF/DX at x=2. The tutorial continues with determining the inverse function and evaluating F inverse of -6. Finally, it explains how to find the derivative of the inverse function at y=F(2), using the relationship between derivatives of functions and their inverses.

What is the value of F(2) for the function F(x) = -2x^3 + 10?

• 0

• 6

• 10

• -6

What is the first step in finding the derivative of F(x) = -2x^3 + 10?

• Subtract 1 from the exponent

• Multiply by 2

• Add 10

• Multiply by 3

What is the value of F'(2) for the function F(x) = -2x^3 + 10?

• -24

• 24

• -12

• 12

How do you express the inverse function of F(x) = -2x^3 + 10?

• x = (10 - y)^(1/3)

• x = (5 + 12y)^(1/3)

• x = (10 + y)^(1/3)

• x = (5 - 12y)^(1/3)

What is the value of F inverse of -6?

• 2

• -2

• 6

• -6

What is the formula for finding the inverse of a function?

• Integrate the function

• Differentiate the function

• Replace x with y and solve for x

• Replace y with x and solve for y

What is the cube root of 8?

• 4

• 2

• 16

• 8

What is the result of substituting -6 into the inverse function F inverse of y?

• -2

• 2

• 6

• -6

What is the relationship between the derivatives of a function and its inverse?

• They are squares

• They are equal

• They are reciprocals

• They are negatives

What is the derivative of F inverse at F(2) if F'(2) = -24?

• -1/4

• -1/24

• 1/24

• 1/4