Gr12 Mathematics: Ch 5.4 Equations of a Tangent to a Curve

What is the relationship between the gradient of a curve and the gradient of the tangent to the curve at a given point?

The gradient of the curve is double the gradient of the tangent.

The gradient of the curve is perpendicular to the gradient of the tangent.

The gradient of the curve is half the gradient of the tangent.

The gradient of the curve is equal to the gradient of the tangent. (correct)

What is the purpose of finding the derivative of a function in determining the equation of a tangent to a curve?

To find the equation of the curve.

To find the normal to the curve.

To find the gradient of the tangent. (correct)

To find the coordinates of the given point.

What is the relationship between the gradients of the tangent and the normal to a curve at a given point?

The gradients are perpendicular.

The product of the gradients is -1. (correct)

The sum of the gradients is 0.

The gradients are equal.

What is the fourth step in determining the equation of a tangent to a curve?

Solve for y to get the equation of the tangent. Signup and view all the answers

What is the first step in determining the equation of a tangent to a curve?

Find the derivative using the rules of differentiation. Signup and view all the answers

What is the purpose of finding the equation of a tangent to a curve?

To find the relationship between the curve and the tangent. Signup and view all the answers

What is the role of the derivative in determining the equation of a tangent to a curve?

To describe the gradient of the curve at any point Signup and view all the answers

Which of the following is NOT a step in determining the equation of a tangent to a curve?

Find the area under the curve Signup and view all the answers

What is the purpose of substituting the x-coordinate of the given point into the derivative?

To find the gradient of the tangent to the curve Signup and view all the answers

Which equation is used to find the equation of a tangent to a curve?

The straight line equation Signup and view all the answers

What is the relationship between the gradients of the tangent and the normal to a curve at a given point?

Their product is -1 Signup and view all the answers

What is the significance of the gradient of the tangent to a curve at a given point?

It is equal to the gradient of the curve at that point Signup and view all the answers

Which of the following statements is true about the gradient of the tangent to a curve?

It is always equal to the gradient of the curve at the same point. Signup and view all the answers

What is the purpose of substituting the x-coordinate of the given point into the derivative?

To find the gradient of the tangent at the given point. Signup and view all the answers

What is the relationship between the gradients of the tangent and the normal to a curve at a given point?

Their product is always equal to -1. Signup and view all the answers

What is the equation of a tangent to a curve used for?

To find the maximum or minimum points of the curve. Signup and view all the answers

What is the significance of the gradient of the tangent to a curve at a given point?

It indicates the direction of the curve at that point. Signup and view all the answers

Gr12 Mathematics: Ch 5.4 Equations of a Tangent to a Curve

Questions and Answers

What is the relationship between the gradient of a curve and the gradient of the tangent to the curve at a given point?

What is the purpose of finding the derivative of a function in determining the equation of a tangent to a curve?

What is the relationship between the gradients of the tangent and the normal to a curve at a given point?

What is the fourth step in determining the equation of a tangent to a curve?

What is the first step in determining the equation of a tangent to a curve?

What is the purpose of finding the equation of a tangent to a curve?

What is the role of the derivative in determining the equation of a tangent to a curve?

Which of the following is NOT a step in determining the equation of a tangent to a curve?

What is the purpose of substituting the x-coordinate of the given point into the derivative?

Which equation is used to find the equation of a tangent to a curve?

What is the relationship between the gradients of the tangent and the normal to a curve at a given point?

What is the significance of the gradient of the tangent to a curve at a given point?

Which of the following statements is true about the gradient of the tangent to a curve?

What is the purpose of substituting the x-coordinate of the given point into the derivative?

What is the relationship between the gradients of the tangent and the normal to a curve at a given point?

What is the equation of a tangent to a curve used for?

What is the significance of the gradient of the tangent to a curve at a given point?

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