Equations of Tangents and Normals

The video tutorial covers finding gradients by differentiating functions, specifically focusing on y = x^2 and y = 4x^3 + 2x^2 - 3x + 2. It explains how to find equations of tangents and normals, solve quadratic equations, and determine where these lines intersect the axes. The tutorial also discusses finding tangents parallel to a given line and emphasizes the relationship between gradients of perpendicular lines.

What is the product of the gradients of two perpendicular lines?

• 0

• 1

• -1

• 2

If y = x^2, what is the gradient of the tangent at x = 6?

• 18

• 12

• 6

• 24

What is the equation of the tangent line to y = x^2 at the point (6, 36)?

• y = 6x + 36

• y = 6x - 36

• y = 12x + 36

• y = 12x - 36

For the curve y = 4x^3 + 2x^2 - 3x + 2, what is the gradient of the tangent line parallel to y = 5x - 4?

• 4

• 6

• 3

• 5

What are the x-values where the tangent to y = 4x^3 + 2x^2 - 3x + 2 is parallel to y = 5x - 4?

• -2 and 1/3

• 2 and -1/3

• 1 and -2/3

• -1 and 2/3

What is the equation of the tangent line that crosses the positive y-axis for the curve y = 4x^3 + 2x^2 - 3x + 2?

• y = 5x - 8

• y = 5x + 8

• y = 5x - 22/27

• y = 5x + 22/27

What is the gradient of the normal line if the tangent's gradient is 5?

• -1/5

• 5

• -5

• 1/5