Functions
Local extrema of absolute value function
MJMT_Full_Test_02
Grade 12
Question:
The function $f(x)=2|x|+|x+2|-\big||x+2|-2|x|\big|$ has a local minima and a local maxima respectively at $x=$
$-2$ and $0$
$-2$ and $2$
$0$ and $-\dfrac{2}{3}$
$0$ and $2$
Step-by-Step Solution
Key Concept: Split into cases at $x=0,-2$. In each region simplify $f(x)$ and find sign changes of $f'$.
Local minima at $x=0$, local maxima at $x=-2/3$.
Correct Answer: 3