Question

Answer 1

a) Do \(3\sqrt{x}\ge0\)

 \(\Rightarrow P=3\sqrt{x}-7\ge-7\)

\(minP=-7\Leftrightarrow x=0\)

b) Do \(\dfrac{1}{2}\sqrt{x}\ge0\)

\(\Rightarrow M=4+\dfrac{1}{2}\sqrt{x}\ge4\)

\(minM=4\Leftrightarrow x=0\)

c) \(F=x+2\sqrt{x}+5=\left(x+2\sqrt{x}+1\right)+4=\left(\sqrt{x}+1\right)^2+4\ge1+4=5\)

\(minF=5\Leftrightarrow\sqrt{x}=0\Leftrightarrow x=0\)

d) \(C=9x+6\sqrt{x}+5=\left(9x+6\sqrt{x}+1\right)+4=\left(3\sqrt{x}+1\right)^2+4\ge1+4=5\)

\(minC=5\Leftrightarrow3\sqrt{x}=0\Leftrightarrow x=0\)