Exponential quotients and stationary points: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{5 e^{x}}{x + 2}\), with \(x>-2\).
Find f′(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{2 e^{2 x}}{x + 3}\), with \(x>-3\).
Find f′(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{2 e^{2 x}}{x + 3}\), with \(x>-3\).
Find f″(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{3 e^{3 x}}{x + 4}\), with \(x>-4\).
Find f″(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{3 e^{3 x}}{x + 4}\), with \(x>-4\).
Find f(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{4 e^{x}}{x + 5}\), with \(x>-5\).
Find f(0).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{4 e^{x}}{x + 5}\), with \(x>-5\).
Find the x-coordinate of the stationary point in x>-5.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Exponential quotients and stationary points: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Let \(\displaystyle f(x)=\frac{5 e^{2 x}}{x + 6}\), with \(x>-6\).
Find the x-coordinate of the stationary point in x>-6.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.