Maths4U Original · Short practice

Let \(f(x)=4 \log{\left(x + 4 \right)}\), with \(x>-4\).

Find f′(0).

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

Maths4U Original · Short practice

Let \(f(x)=5 \log{\left(2 x + 5 \right)}\), with \(\displaystyle x>- \frac{5}{2}\).

Find f′(0).

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

Maths4U Original · Short practice

Let \(f(x)=5 \log{\left(2 x + 5 \right)}\), with \(\displaystyle x>- \frac{5}{2}\).

Find f″(0).

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

Maths4U Original · Short practice

Let \(f(x)=2 \log{\left(3 x + 1 \right)}\), with \(\displaystyle x>- \frac{1}{3}\).

Find f″(0).

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

Maths4U Original · Short practice

Let \(f(x)=2 \log{\left(3 x + 1 \right)}\), with \(\displaystyle x>- \frac{1}{3}\).

Find the x-coordinate of the vertical asymptote.

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

Maths4U Original · Short practice

Let \(f(x)=3 \log{\left(x + 2 \right)}\), with \(x>-2\).

Find the x-coordinate of the vertical asymptote.

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

Maths4U Original · Short practice

Let \(f(x)=3 \log{\left(x + 2 \right)}\), with \(x>-2\).

Find the gradient where the logarithm argument equals one.

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

Maths4U Original · Short practice

Let \(f(x)=4 \log{\left(2 x + 3 \right)}\), with \(\displaystyle x>- \frac{3}{2}\).

Find the gradient where the logarithm argument equals one.

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