Recent questions tagged multiple-selects

Let $p$ be twice differentiable on $\mathbb{R}$ such that $p''(x)>0$ for every real number $x$. Also suppose $p(1)=p(5)=7$. Which of the following statements must be true...

Let $f$ be twice differentiable on $\mathbb{R}$ and suppose $f''(x)>0$ for every real number $x$. Which of the following statements are always true?$f$ has at most one cr...

Let $F(x)=\max\{x^2-6x+8,\ 2x-7,\ 1-x\}$. Which of the following statements is/are true?$F$ is differentiable at its global minimum. The minimum value of $F$ is $-1$. The...

A committee has $10$ members. Some pairs of members know each other, and no three members are mutually strangers. Which of the following statements must be true?The numbe...

Let $A$ and $B$ be non-empty sets and let $f:A\to B$ be a function. For $S\subseteq A$, define $S^c=A-S$. For $Y\subseteq B$, define $Y^c=B-Y$. Which of the following sta...

Let $p:\mathbb R\to\mathbb R$ be continuous at $x=2$ and suppose $p(2)=3$. For a real number $\lambda$, define $q:\mathbb R\to\mathbb R$ by $q(y)=\dfrac{y^2-9}{y-3}$ for ...

The figure shows the graph of $y=F'(x)$ for a differentiable function $F$ on $(-5,6)$. From the graph, $F'(x)=0$ at $x=-3,-1,2,5$. Also, $F'$ has local extrema at $x=-2,1...

Let $f$ be a differentiable function on $\mathbb R$ such that $f'(x)=\dfrac{(x+2)^3(x-1)^2(5-x)}{x^2+1}$. Which of the following statements is/are true?$f$ is strictly in...