MATH100 December 2016
Other MATH100 Exams

### Question 07 (a)

Let ${\displaystyle f(x)}$ be a continuous function on the open interval ${\displaystyle (a,b)}$. Which of the following four statements are always true?
Select all that apply.

1. If ${\displaystyle \lim _{x\to a+}f(x)=-\infty }$ and ${\displaystyle \lim _{x\to b-}f(x)=\infty }$, then there is at least one zero of ${\displaystyle f(x)}$ inside ${\displaystyle (a,b)}$.

2. If ${\displaystyle f(x)}$ has a local minimum at ${\displaystyle c}$ in ${\displaystyle (a,b)}$, then ${\displaystyle f'(c)=0}$.

3. ${\displaystyle f(x)}$ must have both maximum and minimum inside ${\displaystyle (a,b)}$.

4. If ${\displaystyle f''(c)>0}$ for some point ${\displaystyle c}$ in ${\displaystyle (a,b)}$, then ${\displaystyle f(x)}$ has a local minimum at ${\displaystyle c}$.

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