Browse Questions

Find the maximum and minimum values, if any, of the following functions given by?$f(x)=-(x-1)^2+10$

$\begin{array}{1 1}Maximum = 6 Minimum= 5 \\Minimum = 7 \\Maximum= 0 \\ No \;finite\; minima , Maximum=10\end{array}$

Toolbox:
• $f$ is said to have a maximum value in $I$ , if there exist a point c in I such that $f(c) \geq f (x)$ for all $x \in I$.The number $f( c)$ is called the maximum value of f in I and the point c is called a point of maximum value of f in I
• $f$ is said to have a minimum value in $I$ , if there exist a point $c$ in I such that $f(c) \leq f (x)$ for all $x \in I$.The number $f(c)$ is called the minimum value of f in I and the point $c$ in this case is called a point of minimum value of $f$ in I
• $f$ is said to have a extreme value in $I$ , if there exist a point $c$ in I such that f(c) is either a maximum value or minimum value of $f$ in $I$. The number $f (c)$ in this case is called the extreme value of $f$ in $I$ and the point $c$ is called the extreme point.
$f(x)=-(x-1)^2+10$
Maximum value of $-(x-1)^2$ is zero.
$\therefore$ maximum value of $f(x)=-(x-1)^2+10$ is 10.
$f(x)$ does not have any finite minimum value.