Thread: Application of linear approximnation

1. Application of linear approximnation

Also this question which I kind of know how to do but can't get anywhere:
The profit P for a cerain manufacturer selling x items is
P(x) = 200xe^(-x/400)
Use calculus to estimate the change in P as the number of items changes from x=100 to x=105 items.

Thanks

2. Stupid problem

$P'(x)=e^{-x/400}(200-x/2)$ So, $P'(100)=150e^{-1/4}\approx 116.82011746071$ Since the function at this point x=100 can be approximated by a line of this slope, $\Delta P\approx P'(100)\Delta x \approx 117*5 = 585$

This problem is stupid. It's two and a half times harder than just plugging in the two values outright and it's off by about 2%