Finding the Equation of the Normal

The video tutorial explains how to find the equation of the normal to a tangent at a specific point on a function. It begins by defining tangents and normals, highlighting their properties and relationships. The tutorial then demonstrates how to calculate the gradient of the tangent using derivatives and find the gradient of the normal by taking the negative reciprocal. Finally, it shows how to formulate the equation of the normal using point-gradient form and suggests graphing the equation for verification.

What is the relationship between a tangent and a normal?

• They are parallel to each other.

• They never intersect.

• They intersect at a 90-degree angle.

• They have the same gradient.

What is the first step in finding the gradient of a tangent?

• Draw the graph.

• Find the y-intercept.

• Use the derivative of the function.

• Calculate the negative reciprocal.

How do you find the gradient of the normal once you have the gradient of the tangent?

• Multiply by 2.

• Add 1.

• Take the negative reciprocal.

• Divide by 2.

What form is used to calculate the equation of the normal?

• Vertex form

• Point-gradient form

• Slope-intercept form

• Standard form

What is the purpose of multiplying through by a constant when simplifying the equation of the normal?

• To change the slope

• To find the x-intercept

• To eliminate fractions

• To find the y-intercept

Why is it useful to sketch a graph of the equation of the normal?

• To calculate the area under the curve

• To determine the maximum and minimum points

• To verify the alignment with the parabola

• To find the exact coordinates of the intercepts

What does the graph of the equation of the normal help verify?

• The accuracy of the derivative

• The y-intercept of the function

• The correctness of the equation

• The slope of the tangent

What is the final step in finding the equation of the normal?

• Graph the equation

• Calculate the derivative

• Simplify the equation

• Find the x-intercept

What is the importance of taking the negative reciprocal in this process?

• To ensure perpendicularity

• To calculate the slope

• To determine the x-intercept

• To find the y-intercept

What is the main goal of the process described in the video?

• To find the area under the curve

• To determine the maximum point

• To find the equation of the normal

• To calculate the y-intercept