# How do you find the absolute and local extreme values for y=-x+7 on the interval [-10,10]?

Jan 15, 2017

Absolute maximum (point): $\left(- 10 , 17\right)$, and $y = 17$ maximum value
Absolute minimum (point): $\left(10 , - 3\right)$, and $y = - 3$ minimum value

#### Explanation:

$y = - x + 7$ is a line, meaning it has no absolute or local extreme values. However, since we are restricting it to the interval $\left[- 10 , 10\right]$, and the slope is negative, we see that the points with $x$ coordinates $- 10$ or $10$, are the absolute maximum and absolute minimum points, respecitvely. The absolute maximum in this interval is, therefore, $\left(- 10 , 17\right)$ and the absolute minimum is $\left(10 , - 3\right)$.

Trying to use the first derivative doesn't help, since it's always $- 1$, so it is never zero, and always defined.
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