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.

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.

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.

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.

Maths4U Original · Short practice

Consider \(y=- 27 x + \left(x - 1\right)^{3} + 48\).

Find the height of the local maximum.

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

Maths4U Original · Short practice

Consider \(y=- 6 x + 2 \left(x - 2\right)^{3} + 34\).

Find the height of the local maximum.

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

Maths4U Original · Short practice

Consider \(y=- 6 x + 2 \left(x - 2\right)^{3} + 34\).

Find the height of the local minimum.

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

Maths4U Original · Short practice

Consider \(y=- 36 x + 3 \left(x - 3\right)^{3} + 131\).

Find the height of the local minimum.

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