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

The absolute minimum value is "
`-(21)/(4)`" and the absolute maximum value is "
`15`".

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=(1)/(2)` (Critical point)

When x=0,

⇒
`f(x)=-5`

When
`x=(1)/(2)`,

⇒
`f(x)=-(21)/(4)` (Absolute minimum)

When
`x=5`

⇒
`f(x)=15` (Absolute maximum)