Find the values where the function has horizontal tangents

The video tutorial explains how to find horizontal asymptotes and tangents by rewriting a function and applying the chain rule to find its derivative. The process involves simplifying the derivative and solving for when it equals zero to identify horizontal tangents. The tutorial concludes with a brief mention of finding the vertex.

What is the first step in simplifying the function to find horizontal asymptotes?

• Differentiate the function immediately

• Rewrite the function using exponent rules

• Apply the chain rule directly

• Rewrite the function using logarithms

When applying the chain rule, what do you do with the exponents?

• Add them together

• Subtract them

• Multiply them

• Divide them

What is the simplified form of the derivative after applying the chain rule?

• 4X over three times the square root of X^2 - 1

• 4X over three times the cube root of X^2 - 1

• 2X over three times the cube root of X^2 - 1

• 2X over three times the square root of X^2 - 1

How do you solve for x when the derivative is in the denominator?

• Add the denominator to both sides

• Multiply by the denominator on both sides

• Divide by the denominator on both sides

• Subtract the denominator from both sides

At what value of x does the horizontal tangent occur?

• x = 1

• x = 0

• x = 2

• x = -1