Question

Let $f\left(x\right)=\{\begin{array}{cc}{x}^2+x,& -1\le x<0\\ 1,& x=0\\ {\log }_{\frac{1}{2}}(x+\frac{1}{2}),& 0<x<\frac{3}{2}\end{array}$

• A. No global minima occurs
• B. No global maxima occurs
• C. Global minima will occur at $x=-\frac{1}{2}$
• D. Global maxima will occur at $x=0$ and equal to $1$

Answer 1

Answer: (A), (D)

Global maxima will occur at $x=0$ and equal to $1$

Graph of $y=f\left(x\right)$

From figure;
$\Rightarrow$Global maxima is $1,$ which occurs at $x=0$
$\Rightarrow$Global minima doesn't exist.