How to find the slope of a tangent line using the definition of derivative

The video tutorial explains how to identify the slope of an equation by using the limit definition of a derivative. It starts with defining the functions f(x) and f(x+h), then expands the binomial using the FOIL method. The tutorial proceeds to simplify the limit expression and concludes by determining the slope as a function of 2x. The process emphasizes the importance of understanding binomial expansion and limit simplification.

What is the formula used to find the slope of a function using limits?

• m = limit as h approaches 0 of (f(x) - f(x + h))/h

• m = limit as h approaches 0 of (f(x + h) - f(x))/h

• m = limit as x approaches 0 of (f(x + h) - f(x))/h

• m = limit as h approaches 0 of (f(x + h) + f(x))/h

What is the expression for f(x) if f(x) = x^2?

• f(x) = x^3

• f(x) = x + h

• f(x) = x^2

• f(x) = 2x

How do you expand (x + h)^2 using the FOIL method?

• x^2 + 2xh

• x^2 + 2x + h^2

• x^2 + 2xh + h^2

• x^2 + h^2

What happens to the expression after factoring out h and applying direct substitution?

• The expression becomes 2x + h

• The expression becomes 0

• The expression becomes 2x

• The expression becomes h

What is the final expression for the slope as a function of x?

• Slope = x

• Slope = 2x

• Slope = x^2

• Slope = h