Understanding Normal Lines and Tangent Lines

The video tutorial explains how to find the equation of the normal line to the function f(x) = e^x / x^2 at x = 1. It covers the concept of tangent and normal lines, emphasizing that the slope of the normal line is the negative reciprocal of the tangent line's slope. The tutorial demonstrates how to calculate the derivative to find the tangent line's slope and then use it to determine the normal line's equation.

What is the function f(x) that we are working with in this video?

• f(x) = e^x * x^2

• f(x) = x^2 / e^x

• f(x) = e^x / x^2

• f(x) = x^2 - e^x

What is the relationship between the slopes of the tangent and normal lines?

• They are both positive.

• They are both zero.

• They are negative reciprocals of each other.

• They are equal.

Which rule is used to find the derivative of the function f(x) = e^x * x^(-2)?

• Sum Rule

• Chain Rule

• Product Rule

• Quotient Rule

What is the slope of the tangent line at x=1?

• e

• -e

• 1/e

• -1/e

What is the slope of the normal line at x=1?

• e

• -e

• 1/e

• -1/e

What is the general form of the equation of a line?

• y = mx + b

• y = ax^2 + bx + c

• y = mx^2 + c

• y = a/x + b

What point does the normal line pass through when x=1?

• (e, e)

• (e, 1)

• (1, e)

• (1, 1)

How do you solve for the y-intercept 'b' in the line equation y = mx + b?

• Use a known point and solve for b

• Set x to zero and solve for y

• Use the slope directly

• Set y to zero and solve for x

What is the final equation of the normal line derived in the video?

• y = 1/e * x + e - 1/e

• y = -e * x + b

• y = e^2 * x + 1/e

• y = e * x + b

What is the value of b in the normal line equation?

• e^2 - 1/e

• 1/e - e

• e - 1/e

• e + 1/e