Implicit functions · Short practice

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Recall

Implicit first and second derivatives — objective 1

Maths4U Original · Short practice

The curve \(x^2+1y^2=365\) passes through \((13,14)\).

Find \(\displaystyle \frac{dy}{dx}\) at the point.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Implicit first and second derivatives — objective 1

Maths4U Original · Short practice

The curve \(x^2+2y^2=646\) passes through \((14,15)\).

Find \(\displaystyle \frac{dy}{dx}\) at the point.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Implicit first and second derivatives — objective 2

Maths4U Original · Short practice

The curve \(x^2+2y^2=646\) passes through \((14,15)\).

Find \(\displaystyle \frac{d^{2}y}{dx^{2}}\) at the point.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Implicit first and second derivatives — objective 2

Maths4U Original · Short practice

The curve \(x^2+3y^2=993\) passes through \((15,16)\).

Find \(\displaystyle \frac{d^{2}y}{dx^{2}}\) at the point.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Implicit first and second derivatives — objective 3

Maths4U Original · Short practice

The curve \(x^2+3y^2=993\) passes through \((15,16)\).

Find the tangent y-intercept.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Implicit first and second derivatives — objective 3

Maths4U Original · Short practice

The curve \(x^2+4y^2=1412\) passes through \((16,17)\).

Find the tangent y-intercept.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Implicit first and second derivatives — objective 4

Maths4U Original · Short practice

The curve \(x^2+4y^2=1412\) passes through \((16,17)\).

Find the normal gradient.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Implicit first and second derivatives — objective 4

Maths4U Original · Short practice

The curve \(x^2+1y^2=613\) passes through \((17,18)\).

Find the normal gradient.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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