The gradient function and power rule · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Gradients and the power rule — objective 1

Maths4U Original · Short practice

Let \(f(x)=4 x^{2} + 4 x + 19\), with real x.

Find f′(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Gradients and the power rule — objective 1

Maths4U Original · Short practice

Let \(f(x)=5 x^{3} + 5 x + 20\), with real x.

Find f′(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Gradients and the power rule — objective 2

Maths4U Original · Short practice

Let \(f(x)=5 x^{3} + 5 x + 20\), with real x.

Find f″(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Gradients and the power rule — objective 2

Maths4U Original · Short practice

Let \(f(x)=2 x^{4} + x + 21\), with real x.

Find f″(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Gradients and the power rule — objective 3

Maths4U Original · Short practice

Let \(f(x)=2 x^{4} + x + 21\), with real x.

Find f(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Gradients and the power rule — objective 3

Maths4U Original · Short practice

Let \(f(x)=3 x^{2} + 2 x + 22\), with real x.

Find f(1).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Gradients and the power rule — objective 4

Maths4U Original · Short practice

Let \(f(x)=3 x^{2} + 2 x + 22\), with real x.

Find the y-intercept of the tangent at \(\displaystyle x=1\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Gradients and the power rule — objective 4

Maths4U Original · Short practice

Let \(f(x)=4 x^{3} + 3 x + 23\), with real x.

Find the y-intercept of the tangent at \(\displaystyle x=1\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →