Question

Find the absolute maximum and absolute minimum values, if any, of the function. (If an answer does not exist, enter DNE.)f(x) = x2 − x − 5 on [0, 5]

Answer 1

Answer:

The absolute minimum value is "$-\frac{21}{4}$" and the absolute maximum value is "$15$".

Step-by-step explanation:

Given:

$f(x)=x^2-x-5$

on,

$[0,5]$

By differentiating it, we get

⇒ $f'(x)=2x-1$

Set $f'(x)=0$

then,

⇒ $2x-1=0$

          $2x=1$

            $x=\frac{1}{2}$ (Critical point)

When x=0,

⇒ $f(x)=-5$

When $x=\frac{1}{2}$,

⇒ $f(x)=-\frac{21}{4}$ (Absolute minimum)

When $x=5$

⇒ $f(x)=15$ (Absolute maximum)