Question

Determine whether the function has a minimum or maximum value and then find that value.()=−^2+2−7

Answer 1

Given function is

`f(x)=-x^2+2x-7`

Now,

`\begin{gathered} f(x)=-(x^2-2x+7) \\ =-(x^2-2x+1+6) \\ =-\lbrack(x-1)^2+6\rbrack \\ =-(x-1)^2-6 \end{gathered}`

Being a perfect square,

`(x-1)^2\ge0`

Therefore,

`-(x-1)^2\leq0`

So,

`f(x)\leq-6`

Theerfore, the maximum value of the given function is -6.