Answer
See the explanation below.
Work Step by Step
a) A function $f(x)$ that is continuous on a closed interval $[m,n]$, will have a local maximum at $x=x_0$ when $f(x_0) $ is greater than all the enclosing values of the function $f(x)$.
b) A function $f(x)$ that is continuous on a closed interval $[m,n]$, will have a local minimum at $x=x_0$ when $f(x_0)$ is less than all the enclosing values of the function $f(x)$.
c. A function $f(x)$ that is continuous on a closed interval $[a,b]$, will have an absolute maximum at $x=x_0$ when $f(x_0)$ is greater or equal to all the enclosing values of the function $f(x)$. The value of $f(x_0)$ must be an absolute maximum value of $f(x)$.
d. A function $f(x)$ that is continuous on a closed interval $[a,b]$, will have an absolute minimum at $x=x_0$ when $f(x_0)$ is less than or equal to all the enclosing values of the function $f(x)$. The value of $f(x_0)$ must be an absolute minimum value of $f(x)$.
