5.6 Stationary points Quiz

1. $f(x)=x^2-4x+7$. At which value of $x$ is $f'(x)=0$?

• A. $x=-2$
• B. $x=4$
• C. $x=2$
• D. $x=7$

2. The gradient changes from negative to positive at a stationary point. This is:

• A. a local minimum
• B. a local maximum
• C. neither a maximum nor a minimum
• D. the greatest value of the function

3. What are the coordinates of the stationary point of $f(x)=x^2-4x+7$?

• A. $(3,2)$
• B. $(2,0)$
• C. $(2,7)$
• D. $(2,3)$

4. $f$ has a local maximum at $x=a$. Which statement is correct?

• A. $f(a)$ is the greatest value of $f$ on the whole domain
• B. $f'(a)=0$ and $f(a)$ is the greatest value of $f$ near $x=a$
• C. $f(a)=0$
• D. $f'(a)$ is the maximum gradient

5. $f$ has a local minimum at $x=4$ with $f(4)=7$. On the domain $0\le x\le10$, $f(10)=3$. Which statement is correct?

• A. The least value of $f$ is 7
• B. The least value of $f$ is 4
• C. The least value of $f$ is at most 3, so the local minimum is not the least value
• D. $f(4)$ is least because $f'(4)=0$