Find the absolute maximum and absolute minimum values of `f(x)=(x-1)^2+3` in `[-3,\ 1]`

Options

A. absolute maximum = 19
absolute minimum = 3
B. absolute maximum = 16
absolute minimum = 3
C. absolute maximum = 3
absolute minimum = 19
D. None of these

Answer

A

Explanation

`f(x)=(x-1)^2+3`

`f prime (x)= 2(x-1)`

for critical points `f prime (x) =0`


`x=1`

`f(-3)=(-3-1)^2 +3`

`f(-3)=19`

`f(1)=(1-1)^2 +3`

...