Question

Please help!

Answer 1

Find its maximum or minimum value.
\[f(x)=\frac{ -x^2 }{ 3 }+2x+7\]

Answer 2

\[f'(x)=\frac{ -2x }{3 }+2\]
f'(x)=0 gives
\[\frac{ -2x }{ 3 }+2=0,\frac{ -2x }{ 3 }=-2,x=-2*\frac{ 3 }{ -2 }=3\]
\[f''(x)=\frac{ -2 }{ 3 }\]
At x=3,
\[f''(x)=-\frac{ 2 }{ 3 }<0\]
Hence there is maxima at x=3
there is no minimum value.

Answer 3

put x=3 in f(x) and get the maximum value.