# Find the Absolute Max and Min over the Interval f(x)=8-x , (-3,5)

,
Find the first derivative.
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Subtract from .
Set the first derivative equal to zero.
Since , there are no solutions.
No solution
Since there is no value of that makes the first derivative equal to , there are no local extrema.
No Local Extrema
Compare the values found for each value of in order to determine the absolute maximum and minimum over the given interval. The maximum will occur at the highest value and the minimum will occur at the lowest value.
Absolute Maximum:
Absolute Minimum:
Find the Absolute Max and Min over the Interval f(x)=8-x , (-3,5)