Hello, weasley74!
Replace withFind the biggest and smallest values of: .
without using the derivative.
We have: .
Let
This is a down-opening parabola; its maximum is at its vertex.
. . The vertex is at: .
Hence, the maximum is: .
Normally, there is no minimum for this parabola.
. . However, the values of are limited: .
The minimum occurs at an endpoint of the interval.
. . And we find that the minimum is: .
Are you familiar with parabolas? Do you know how to find the turning point of a parabola?
There are many ways to get the turning point - Soroban gave one which clearly you're not familiar with. What about completing the square to get turning point form? You've gotta have met that one ....?
.
Maximum turning point at , that is, f(u) has a maximum value of (corresponding to .....)