Me i don’t know how to get started!

A differentiable function is increasing on an open interval if for all , and decreasing if . For this problem, you then need to compute the derivative:

then solve for :

We can ignore because is defined only for . So we have two intervals to consider, and . All we need to do is pick any value from either interval and check the sign of the derivative . Since , from the first interval we can take , and from the second we can pick .

The above indicates that is decreasing on the first interval , and increasing on the second interval .

For part (b), we use the info from above as part of the first derivative test for extrema. We have one critical point at , and we know how behaves to either side of this point; decreases to left of it, and increases to the right. This pattern is indicative of a minimum occurring at , and we find that has the (local) minimum value of .

1gm = 1000mg so 0.1gm = 1000mg

first, convert the weight to kg

160lb * 1kg/2.2lb = 72.7kg

next, the dose

72.7kg * 100mg/kg = 7270mg