Question

If P'(x)=50-.10x and P(0)=-500, find P(200)

Answer 1

`P'(x)=50-0.10x`

`\implies P(x)=\displaystyle\int(50-0.10x)\,\mathrm dx`

`P(x)=50x-\frac{0.10}2x^2+C`

`P(x)=50x-0.05x^2+C`

Given that
`P(0)=-500`, we have


`-500=50(0)-0.05(0)^2+C\implies C=-500`

and so


`P(x)=50x-0.05x^2-500`

which means that


`P(200)=50(200)-0.05(200)^2-500`

`P(200)=7500`