Understanding Derivatives and Tangent Lines

The video tutorial explains how to find the derivative of the function g(x) = 2/x^3 - 1/x^2 using the power rule and basic exponent properties. It then evaluates the derivative at x = 2 to find the slope of the tangent line to the graph of g at that point. The process involves rewriting the function in terms of negative exponents, applying the power rule, and simplifying the result to find the slope as -1/8.

What is the main goal of the video tutorial?

• To find the integral of g(x)

• To find the derivative of g(x) and evaluate it at x=2

• To solve the equation g(x) = 0

• To graph the function g(x)

How can the term 2/x^3 be rewritten using exponent properties?

• 2x^3

• 2x^-3

• x^-3/2

• x^3/2

What is the rewritten form of 1/x^2 using exponent properties?

• 1/x

• x^2

• x^-2

• 2x

Which rule is primarily used to find the derivative of g(x)?

• Product Rule

• Chain Rule

• Quotient Rule

• Power Rule

What is the derivative of 2x^-3 using the power rule?

• -6x^-4

• 6x^-4

• 3x^-2

• -3x^-2

What is the derivative of x^-2 using the power rule?

• -2x^-3

• 2x^-3

• 3x^-2

• -3x^-2

What is the expression for g'(x) after applying the power rule?

• -6x^-4 + 2x^-3

• 6x^-4 - 2x^-3

• 6x^4 - 2x^3

• -6x^4 + 2x^3

What is the value of 2^4?

• 24

• 8

• 12

• 16

What is the slope of the tangent line to the graph of g at x=2?

• 1/8

• -1/8

• 1/4

• -1/4

What is the final result of evaluating g'(2)?

• 1/8

• -1/8

• 1/4

• -1/4