# What are the extrema of f(x)=x^2-192x+8  on x in[-4,9]?

Nov 10, 2015

The minimum is $f \left(9\right)$, and the maximum is $f \left(- 4\right)$.

#### Explanation:

$f ' \left(x\right) = 2 x - 192$, so there are no critical numbers for $f$ in the interval chosen.

Therefore, The minimum and maximum occur at the endpoints.

$f \left(- 4\right) = 16 + 192 \left(4\right) + 8$ is clearly a positive number and $f \left(9\right) = 81 - 192 \left(9\right) + 4$ is clearly negative.

So, the minimum is $f \left(9\right)$, and the maximum is $f \left(- 4\right)$.