Question

Determine the position of all maximum points using the second-derivative test of y=(x^2/6)-2x+8

Answer 1

Is this it?
\[y=\frac{x ^{2}}{6}-2x+8\]

Answer 2

first differentiate y w.r.t x and find the extremities. then find 2nd derivative of y. check whether it is -ve . if it is -ve then the extremum represents maximum

Answer 3

\[f'(x)=\frac{x}{3}-2\]
x/3 - 2 = 0
x = 6
\[f''(x)=\frac{1}{3}\]
f''(x) is positive therefore x = 6 is at a minimum point. There are no maximum points.