Understanding Tangent Lines and Derivatives

The video tutorial explains how to find the equation of a tangent line to a function f(x) = 1/x^2 - Kx, where K is a constant. The process involves setting K to 3, calculating the derivative, and using it to find the slope at a specific point. The tutorial then determines the y-intercept and combines these to form the final equation of the tangent line.

What is the general form of the function f(x) discussed in the video?

• f(x) = x^2 - Kx

• f(x) = x^2 + Kx

• f(x) = 1/x^2 - Kx

• f(x) = 1/x^2 + Kx

What value is assigned to the constant k in the video?

• 5

• 3

• 2

• 4

What is the form of the equation for a line?

• Y = mx + b

• Y = mx - b

• Y = m/x - b

• Y = m/x + b

How is the slope of the tangent line determined?

• By evaluating the derivative at x = 6

• By evaluating the derivative at x = 3

• By evaluating the derivative at x = 4

• By evaluating the derivative at x = 5

What is the value of the slope m when x = 4?

• -5/16

• 5/16

• -3/16

• 3/16

What is the y-coordinate of the point on the curve when x = 4?

• 1/2

• 1/3

• 1/4

• 1/5

What is the value of b, the y-intercept, in the tangent line equation?

• 4.5

• 2.5

• 3.5

• 1.5

What is the final equation of the tangent line?

• y = -5/16x + 1.5

• y = 5/16x + 1.5

• y = -5/16x - 1.5

• y = 5/16x - 1.5

How can the y-intercept 1.5 be expressed as a fraction?

• 3/2

• 2/3

• 2/5

• 5/2

What is the purpose of finding the tangent line to the curve?

• To find the minimum point

• To find the area under the curve

• To find the maximum point

• To find the slope at a specific point