Let g(s)=1/(s-2) on the interval [0,1]. Find the absolute maximum and absolute minimum of g(s) on this interval.
The absolute max occurs at s=.
The absolute min occurs at s=
hint:
find g(0) and g(1)
find where g'(s) = 0, then evaluate g there.
pick the min and max of those values.
i got maximum to be -¼ and minimum to be -1 and i got it wrong
To find the absolute maximum and absolute minimum of the function g(s)=1/(s-2) on the interval [0,1], we can use the concept of critical points and endpoints.
1. Start by checking the value of g(s) at the endpoints of the interval:
At s=0, g(0) = 1/(0-2) = -1/2
At s=1, g(1) = 1/(1-2) = -1
So, the values at the endpoints are -1/2 and -1.
2. Next, find any critical points within the interval [0,1]. Critical points are the values of s where the derivative of g(s) is either zero or does not exist. In this case, since g(s) is a rational function, the derivative can be calculated using the quotient rule:
g'(s) = (-1)/(s-2)^2
Setting the derivative equal to zero, we get:
(-1)/(s-2)^2 = 0
Since the denominator (s-2)^2 cannot be zero, there are no critical points in the interval [0,1].
3. Finally, compare the values obtained at the endpoints with the critical points (which in this case is none) to determine the absolute maximum and absolute minimum:
The absolute maximum is the highest value between the endpoints and the critical points. In this case, the highest value is -1/2, which occurs at s=0.
The absolute minimum is the lowest value between the endpoints and the critical points. In this case, the lowest value is -1, which occurs at s=1.
Therefore, the absolute maximum of g(s) on the interval [0,1] is -1/2 at s=0, and the absolute minimum is -1 at s=1.