Extreme Values Help?

Question

Find the extreme values of the function on the interval and where they occur.

g(x)= -x^2+11x-30 on 5 (less than or equal to) x (less than or equal to) 6

Answer 1

This really depends on what class you're in. It's easiest if you use calculus.

In calculus, you can find exteme values by setting the derivative equal to zero.

-2x + 11 = 0

If you solve that, you get x = 11/2 or 5.5 (which is in the interval from 5 to 6) You can find the y-value by evaluating the function at 5.5 ... the point is (5.5 , .25)

Since the graph is a parabola with a negative coefficient on x^2, the point (5.5 , .25) is an absolute maximum. This is the vertex of the parabola.

There will be two relative minima, which occur when x = 5 and x = 6 (the endpoints of your interval). The y-value at both of these points is 0 ... So (5,0) and (6,0) are minima.