Find the maximum and minimum value of the polynomial f(x)`=-x^(2)+x+2`.

Answer

N/a

Explanation

f(x)`=-x^(2)+x+2=-(x^(2)-xx2)`
`=-(x^(2)-x+(1)/(4)-(1)/(4)-2) " "` [adding and subtracting same quantity i.e., `(("coeff. Of "x)/(2))^(2)]`
`=-[(x-(1)/(2))^(2)-(9)/(4)]=(9)/(4)-(x-(1)/(2))^(2)`
If `x-(1)/(2)=0` then f(x)`=(9)/(4)` is the maximum value.
So, maximum value of f(x)`=(9)/(4)` and minimum value cannot be found in this case. Ans.