Increasing, decreasing and stationary points: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(y=x^3-3x\), find \(y''\) at \(x=1\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Increasing, decreasing and stationary points: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(y=x^3-3x\), what is the nature of the stationary point at \(x=1\)?Choose one answer.
Increasing, decreasing and stationary points: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Where is \(y=x^2-6x+2\) strictly decreasing?Choose one answer.
Increasing, decreasing and stationary points: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
At a stationary point, \(f''(a)=0\). What follows from this second-derivative test alone?Choose one answer.
Increasing, decreasing and stationary points: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(y=x^3-12x\), find the second derivative at \(\displaystyle x=-2\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Increasing, decreasing and stationary points: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(y=x^3-12x\), find the x-coordinate of its local minimum.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Increasing, decreasing and stationary points: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(y=x^2-10x+7\), the decreasing interval is x less than a. Find a.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Increasing, decreasing and stationary points: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
For \(f(x)=x^4\), both first and second derivatives vanish at zero. Find the minimum value of f on [-1,1].Enter one number or fraction. Round decimals to at least six decimal places when needed.