Stationary points and increasing and decreasing functions Quiz

1. Which is the stationary point of $y=x^2-8x+3$?

• A. $(4,-13)$
• B. $(4,3)$
• C. $(-4,51)$
• D. $(8,3)$

2. For which values of $x$ is $\mathrm{f}(x)=x^3-12x$ increasing?

• A. $-2<x<2$
• B. $x<-2$ or $x>2$
• C. $x>2$ only
• D. $x<-2$ only

3. At a stationary point $\frac{d^2y}{dx^2}=-6$. The point is

• A. a minimum
• B. a point of inflection
• C. a maximum
• D. impossible to classify

4. For $y=x^3$, $\frac{dy}{dx}=0$ and $\frac{d^2y}{dx^2}=0$ at $x=0$. This point is

• A. a maximum
• B. a minimum
• C. not a stationary point
• D. a point of inflection

5. The curve $y=x^3-3x+k$ has stationary points $(-1,k+2)$ and $(1,k-2)$. For which $k$ does $y=0$ have three distinct roots?

• A. $k>2$
• B. $-2<k<2$
• C. $k<-2$
• D. $k>2$ or $k<-2$