Question

$f\left(x\right)=x^2-4|x|andg\left(x\right)=\{\begin{array}{c}min\left\{f\right(t):-6\le t\le x\},xϵ[-6,0]\\ max\left\{f\right(t):0\le t\le x\},xϵ[0,6]\end{array},thang\left(x\right)$

• A. Exactly one point of local minima
• B. Exactly one point of local maxima
• C. No point of local maxima but exactly one point of local minima
• D. Neither a point of local maxima nor minima

Answer 1

The correct option is D Neither a point of local maxima nor minima

Bold line represents the graph of y = g(x) clearly g(x) has neither a point of local maxima nor a point of local minima.